Theoretical Distributions

230 Practice MCQs available for CA Foundation

Paper

Paper 3: Quantitative Aptitude

Exam Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

All 230 Questions

3474
Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3
MCQ
3475
When p=0.5\displaystyle p=0.5, the binomial distribution is
MCQ
3476
If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be
MCQ
3477
A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is
MCQ
3478
When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:
MCQ
3517
For a Poisson distribution,
MCQ
3518
For Poisson Distribution :
MCQ
3528
The mean and variance are equal for which of the following:
MCQ
4086
Poisson probability distribution is appropriately applied in
MCQ
4087
If the points of inflexion of a normal curve are 6 and 14, then standard deviation of the distribution is
MCQ
4088
What is the probability of making 3 corrected guesses in 5 True-False answer type questions?
MCQ
4089
If 5% of the families in large population city do not use gas as a fuel, what will be the probability of selecting 10 families in a random sample of 100 families who do not use gas as a fuel? [Given that e−5=0.0067\displaystyle e^{-5} = 0.0067]
MCQ
4185
The Mode of binomial distribution B(7,13)\displaystyle B(7, \frac{1}{3}) is
MCQ
4186
An emergency room receives an average of 3 patients per hour. What is the probability that exactly 2 patients arrive in an hour? (Given: e0=1\displaystyle e^0 = 1, e−1=0.367\displaystyle e^{-1} = 0.367, e−2=0.135\displaystyle e^{-2} = 0.135, e−3=0.049\displaystyle e^{-3} = 0.049, e−4=0.018\displaystyle e^{-4} = 0.018, e−5=0.0067\displaystyle e^{-5} = 0.0067)
MCQ
4187
If a binomial distribution has n=20\displaystyle n = 20 and p=0.3\displaystyle p = 0.3 what is its variance?
MCQ
4188
It is given that X\displaystyle X has normal distribution with mean zero and standard deviation one. Also given that P[−2<X<2]=0.95\displaystyle P[-2 < X < 2] = 0.95, P[−2<X<−1.5]=0.045\displaystyle P[-2 < X < -1.5] = 0.045. Find the probability for P[0<x<1.5]\displaystyle P[0 < x < 1.5].
MCQ
4189
The probability mass function of a distribution is given below in a tabular form: p(x)\displaystyle p(x) is k\displaystyle k at x=0\displaystyle x=0, 2k+k2\displaystyle 2k+k^2 at x=1\displaystyle x=1, 3k\displaystyle 3k at x=2\displaystyle x=2, 2k+k2\displaystyle 2k+k^2 at x=3\displaystyle x=3, and k\displaystyle k at x=4\displaystyle x=4. Where k\displaystyle k is a non-negative constant. The median of the distribution is
MCQ
4243
A quality control inspector finds that 20% of light bulbs are defective. If a batch of 5 light bulbs is tested, what is the probability that exactly 1 bulb is defective?
MCQ
4292
For a binomial distribution, if the mean is 10 and the standard deviation is 3, find n. (number of trials)
MCQ
4293
If a binomial distribution has n=25\displaystyle n = 25 and p=0.2\displaystyle p = 0.2 what is its mean?
MCQ
4294
If X is a Poisson variate such that P(X=1)=0.3\displaystyle P(X = 1) = 0.3 and P(X=2)=0.2\displaystyle P(X = 2) = 0.2 then P(X=0)=\displaystyle P(X = 0) =
MCQ
4295
If the first quartile (Q1\displaystyle Q_1) and third quartile (Q3\displaystyle Q_3) of a normal distribution are 22 and 28, what is the median of the distribution?
MCQ
3560
If the quartile deviation of a normal curve is 4.05, then its mean deviation is
MCQ
3537
What is the first quartile of x\displaystyle x having the following probability density function? f(x)=172πe−(x−10)272\displaystyle f(x) = \frac{1}{\sqrt{72\pi}} e^{-\frac{(x-10)^2}{72}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3501
If a Poisson distribution is such that P(X=2)=P(X=3)\displaystyle P(X=2) = P(X=3), then the standard deviation of the distribution is:
MCQ
3973
If 5%\displaystyle 5\% of the electric bulbs manufactured by a company are defective, use Poisson distribution to find the probability that in a sample of 100\displaystyle 100 bulbs, 5\displaystyle 5 bulbs will be defective. [Given : e−5=0.007\displaystyle e^{-5} = 0.007 ]
MCQ
3572
For the normal distribution density function f(x)=Ke−(x−6)28\displaystyle f(x) = K e^{-\frac{(x-6)^2}{8}}, the mean and variance are.
MCQ
3418
If mean and variance are 5\displaystyle 5 and 3\displaystyle 3 respectively then relation between p\displaystyle p and q\displaystyle q is:
MCQ
3441
If X\displaystyle X & Y\displaystyle Y are two independent variables such that XsimB(n1,p)\displaystyle X \\sim B(n_1, p) and YsimB(n2,p)\displaystyle Y \\sim B(n_2, p) then the parameter of Z=X+Y\displaystyle Z = X+Y is
MCQ
3538
If the area of standard normal curve between z=0\displaystyle z=0 to z=1\displaystyle z=1 is 0.3412\displaystyle 0.3412, then the value of ϕ(1)\displaystyle \phi(1) is
MCQ
3427
The incidence of skin diseases in a chemical plant occurs in such a way that the workers have 20%\displaystyle 20\% chance of suffering from it. What is the probability that out of 6\displaystyle 6 workers 4\displaystyle 4 or more will have skin diseases?
MCQ
3420
In a binomial distribution B(n,p)\displaystyle B(n, p), n=4\displaystyle n = 4, P(X=2)=3P(X=3)\displaystyle P(X=2) = 3P(X=3) find p\displaystyle p
MCQ
3563
If X and Y are independent Normal Variables with mean 100 and 80 respectively and standard deviation as 4 and 3 respectively. What is the distribution of (X+Y)\displaystyle (X+Y)?
MCQ
3981
If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean deviation is
MCQ
3982
What is the mean of X having the following density function f(x)=142πe−(x−10)232\displaystyle f(x) = \frac{1}{4\sqrt{2\pi}} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3984
If X follows normal distribution with μ=50\displaystyle \mu = 50 and σ=10\displaystyle \sigma = 10, what is value of P(X≤60∣X>50)\displaystyle P(X \le 60 | X > 50)?
MCQ
4386
Poisson probability distribution is appropriately applied in
MCQ
4387
If the points of inflexion of a normal curve are 6 and 14, then standard deviation of the distribution is
MCQ
4388
What is the probability of making 3 corrected guesses in 5 True-False answer type questions?
MCQ
4389
If 5% of the families in large population city do not use gas as a fuel, what will be the probability of selecting 10 families in a random sample of 100 families who do not use gas as a fuel? [Given that e−5=0.0067\displaystyle e^{-5} = 0.0067]
MCQ
4485
The Mode of binomial distribution B(7,13)\displaystyle B(7, \frac{1}{3}) is
MCQ
4486
An emergency room receives an average of 3 patients per hour. What is the probability that exactly 2 patients arrive in an hour? (Given: e0=1\displaystyle e^0 = 1, e−1=0.367\displaystyle e^{-1} = 0.367, e−2=0.135\displaystyle e^{-2} = 0.135, e−3=0.049\displaystyle e^{-3} = 0.049, e−4=0.018\displaystyle e^{-4} = 0.018, e−5=0.0067\displaystyle e^{-5} = 0.0067)
MCQ
4487
If a binomial distribution has n=20\displaystyle n = 20 and p=0.3\displaystyle p = 0.3 what is its variance?
MCQ
4488
It is given that X\displaystyle X has normal distribution with mean zero and standard deviation one. Also given that P[−2<X<2]=0.95\displaystyle P[-2 < X < 2] = 0.95, P[−2<X<−1.5]=0.045\displaystyle P[-2 < X < -1.5] = 0.045. Find the probability for P[0<x<1.5]\displaystyle P[0 < x < 1.5].
MCQ
4489
The probability mass function of a distribution is given below in a tabular form: p(x)\displaystyle p(x) is k\displaystyle k at x=0\displaystyle x=0, 2k+k2\displaystyle 2k+k^2 at x=1\displaystyle x=1, 3k\displaystyle 3k at x=2\displaystyle x=2, 2k+k2\displaystyle 2k+k^2 at x=3\displaystyle x=3, and k\displaystyle k at x=4\displaystyle x=4. Where k\displaystyle k is a non-negative constant. The median of the distribution is
MCQ
4543
A quality control inspector finds that 20% of light bulbs are defective. If a batch of 5 light bulbs is tested, what is the probability that exactly 1 bulb is defective?
MCQ
4592
For a binomial distribution, if the mean is 10 and the standard deviation is 3, find n. (number of trials)
MCQ
4593
If a binomial distribution has n=25\displaystyle n = 25 and p=0.2\displaystyle p = 0.2 what is its mean?
MCQ
4594
If X is a Poisson variate such that P(X=1)=0.3\displaystyle P(X = 1) = 0.3 and P(X=2)=0.2\displaystyle P(X = 2) = 0.2 then P(X=0)=\displaystyle P(X = 0) =
MCQ
4595
If the first quartile (Q1\displaystyle Q_1) and third quartile (Q3\displaystyle Q_3) of a normal distribution are 22 and 28, what is the median of the distribution?
MCQ
3598
The mean deviation about median of standard normal variate is
MCQ
3599
If the Quartile Deviation of a normal distribution with mean 10\displaystyle 10 and SD 4\displaystyle 4 is
MCQ
3600
If the two Quartiles N(μ,σ2)\displaystyle N(\mu, \sigma^2) are 14.6\displaystyle 14.6 and 25.4\displaystyle 25.4 respectively. What is the standard deviation of the distribution?
MCQ
3601
The wages of workers of a factory follows
MCQ
3602
If the inflexion points of a Normal Distribution are 6\displaystyle 6 and 14\displaystyle 14. Find its SD?
MCQ
3992
For a continuous random variable following standard normal distribution, what is the value of standard deviation?
MCQ
3990
Area between -1.96 to +1.96 in a normal distribution is :
MCQ
3413
The variance of a binomial distribution with parameters n\displaystyle n and p\displaystyle p is:
MCQ
3414
An example of a bi-parametric discrete probability distribution is
MCQ
3415
Probability distribution may be
MCQ
3416
The mean of the Binomial distribution B(4,1/3)\displaystyle B(4, 1/3) is equal to
MCQ
3417
The probability that a student is not a swimmer is 1/5\displaystyle 1/5 then the probability that out of five students four are swimmer is
MCQ
3419
Find mode when n=15\displaystyle n = 15 and p=1/4\displaystyle p = 1/4 in binomial distribution?
MCQ
3421
If the probability of success in a binomial distribution is less than one-half, then the binomial distribution
MCQ
3422
A coin with probability for heads as 1/5\displaystyle 1/5 is tossed 100\displaystyle 100 times. The standard deviation of the number of head 5\displaystyle 5 turned up is.
MCQ
3423
If X\displaystyle X is a binomial variate with p=1/3\displaystyle p = 1/3, for the experiment of 90\displaystyle 90 trials, then the standard deviation is equal to:
MCQ
3424
Four unbiased coins are tossed simultaneously. The expected no. of heads is:
MCQ
3425
For a binomial distribution, there may be -
MCQ
3426
The standard deviation of binomial distribution is:
MCQ
3428
If mean and variance of a random variable which follows the Binomial Distribution are 7\displaystyle 7 and 6\displaystyle 6 respectively, then the probability of success is:
MCQ
3429
If six coins are tossed simultaneously. The probability of obtaining exactly two heads are:
MCQ
3430
For a binomial distribution the mean and standard deviation are 10\displaystyle 10 and 3\displaystyle 3 respectively. Find the value of n\displaystyle n.
MCQ
3431
For a binomial distribution, the variance is 0.2\displaystyle 0.2 and the mean is 0.6\displaystyle 0.6. The probability of getting 3\displaystyle 3 successes out of a trial of 5\displaystyle 5 is _____.
MCQ
3432
When 'p\displaystyle p' =0.5\displaystyle = 0.5, the
MCQ
3433
If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 4\displaystyle 4 respectively, p\displaystyle p will be
MCQ
3434
The mean of Binomial distribution is 4\displaystyle 4 and the Standard Deviation sqrt3\displaystyle \\sqrt{3}, what is the value of p\displaystyle p.
MCQ
3435
The mean of binomial distribution is
MCQ
3436
In Binomial distribution the trails are
MCQ
3437
If p\displaystyle p is increased for a fixed n\displaystyle n; the Binomial distribution shifts to the
MCQ
3438
A binomial distribution is
MCQ
3439
The maximum value of the variance of binomial distribution with parameters n\displaystyle n and p\displaystyle p is
MCQ
3440
The max. value of the variance of binomial distribution with parameters n\displaystyle n and p\displaystyle p is
MCQ
3442
Five coins tossed 3200 times. The number of times 5 heads appeared is.
MCQ
3443
Find the probability of a success for the binomial distribution satisfying the following relation 4P(x=4)=P(x=2)\displaystyle 4 P(x=4) = P(x=2) and having the parameter n\displaystyle n as six.
MCQ
3444
An experiment succeeds thrice as after it fails. If the experiment is repeated 5times, what is the probability of having no success at all?
MCQ
3445
The overall percentage of failures in a certain examination was 30. What is the probability that out of a group 6 candidates at least four passed the examination? Note: Exact Ans is 0.74431
MCQ
3446
What is the probability of getting exactly 2 head in 7 tosses of a fair coin?
MCQ
3447
The Binomial Distribution for which mean = 15 and variance = 6.0 is
MCQ
3448
The SD of a binomial distribution with parameter n\displaystyle n and p\displaystyle p is
MCQ
3449
Bivariate Data are the data collected for Note: From correlation regression chapter.
MCQ
3450
If x\displaystyle x is binomial variate with parameter 15 and 1/3\displaystyle 1/3 what is the value of mode of the distribution.
MCQ
3451
The mean of a binomial distribution with parameter n\displaystyle n and p\displaystyle p is
MCQ
3452
The Binomial distribution n=9\displaystyle n=9 and p=1/3\displaystyle p=1/3. What is the value of the variance?
MCQ
3453
In a Binomial Distribution B(n,p)\displaystyle B(n, p), n=4\displaystyle n=4, then P(x=2)=3P(x=3)\displaystyle P(x=2) = 3 P(x=3). Find p\displaystyle p
MCQ
3454
The variance of a binomial distribution with parameters n\displaystyle n and p\displaystyle p is
MCQ
3455
What is the probability of getting 3 heads if 6 unbiased coins are tossed simultaneously?
MCQ
3456
The mode of the binomial distribution for which the mean is 4 variance 3 is equal to ?
MCQ
3457
If a variate x\displaystyle x has, mean=variance, then the distribution will be _____
MCQ
3458
In a Binomial distribution n=9\displaystyle n=9 and P=13\displaystyle P=\frac{1}{3}, what is the value of Variance.
MCQ
3459
Examine the validity of the following: Mean and standard deviation of a binomial distribution are 10 and 4 respective:
MCQ
3460
The probability of a man hitting the target is 1/4\displaystyle 1/4. If he fires 7 times, the probability of hitting the target at least twice is :
MCQ
3461
If mean and variance are 5 and 3 respectively then relation between p\displaystyle p and q\displaystyle q is
MCQ
3462
If a coin is tossed 5 times then the prob. of getting Tail and Head occurs alternatively is:
MCQ
3463
The probability that a student is not a swimmer is 1/5\displaystyle 1/5, then the probability that out of five students four are swimmers is:
MCQ
3464
A random variable x\displaystyle x follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2. then the value of n\displaystyle n is
MCQ
3465
If x\displaystyle x is binomial with parameter 15\displaystyle 15 and 13\displaystyle \frac{1}{3}, what is mode of the distribution?
MCQ
3466
When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is
MCQ
3467
A die is thrown 100\displaystyle 100 times, if getting an even number is considered a success then the variance number of success.
MCQ
3468
The standard deviation of Binomial distribution is
MCQ
3469
In Binomial distribution n=9\displaystyle n=9 and P=13\displaystyle P=\frac{1}{3}, what is the value of variance?
MCQ
3470
The overall percentage of failure in a certain examination is 0.30\displaystyle 0.30. What is the probability that out of a group of 6\displaystyle 6 candidates at least 4\displaystyle 4 passed the examination?
MCQ
3471
For binomial distribution E(x)=2\displaystyle E(x)=2, V(x)=43\displaystyle V(x)=\frac{4}{3}. Find the value of n\displaystyle n.
MCQ
3472
Parameter is a characteristic of:
MCQ
3473
If mean & variance are 5\displaystyle 5 and 3\displaystyle 3 respectively then relation between p\displaystyle p and q\displaystyle q is:
MCQ
3479
If X\displaystyle X is a binomial variable with parameters n\displaystyle n and p\displaystyle p, then X\displaystyle X can assume
MCQ
3480
X\displaystyle X is a binomial variable such that 2P(X=2)=P(X=3)\displaystyle 2P(X=2)=P(X=3) and Mean of X\displaystyle X is known to be frac103\displaystyle \\frac{10}{3}. What would be the probability that X\displaystyle X assumes at most the value 2\displaystyle 2?
MCQ
3481
In a Poisson distribution if P(X=4)=P(X=5)\displaystyle P(X=4)=P(X=5) then the parameter of Poisson distribution is:
MCQ
3482
For a poisson distribution:
MCQ
3483
In Poisson distribution, if P(X=2)=12P(X=3)\displaystyle P(X=2) = \frac{1}{2}P(X=3) find m\displaystyle m?
MCQ
3484
Which of the following is uni-parametric distribution?
MCQ
3485
Which one of the following has Poisson distribution?
MCQ
3486
For a Poisson distributed variable X\displaystyle X, we have P(X=7)=8P(X=9)\displaystyle P(X=7)=8P(X=9), the mean of the distribution is:
MCQ
3487
If the parameter of Poisson distribution is m\displaystyle m and (Mean+S.D.)=625\displaystyle (Mean + S.D.) = \frac{6}{25} then find m\displaystyle m:
MCQ
3488
X\displaystyle X is a Poisson variate satisfying the following condition 9P(X=4)+30P(X=6)=P(X=2)\displaystyle 9P(X=4)+30P(X=6)=P(X=2). What is the value of P(X≤1)\displaystyle P(X \le 1)?
MCQ
3489
For a Poisson variate X\displaystyle X, P(X=2)=3P(X=4)\displaystyle P(X=2)=3P(X=4), then the standard deviation of X\displaystyle X is
MCQ
3490
4\displaystyle 4 coins were tossed 1600\displaystyle 1600 times. What is the probability that all 4\displaystyle 4 coins do not turn head upward at a time?
MCQ
3491
If X\displaystyle X is a Poisson variable and P(X=1)=P(X=2)\displaystyle P(X=1) = P(X=2), then P(X=4)\displaystyle P(X=4) is
MCQ
3492
Which one of the following is an unparametric distribution?
MCQ
3493
It is Poisson variate such that P(X=1)=0.7,P(X=2)=0.3\displaystyle P(X=1) = 0.7, P(X=2) = 0.3, then P(X=0)=\displaystyle P(X=0) =
MCQ
3494
The average number of advertisements per page appearing in a newspaper is 3. What is the probability that in a particular page zero number of advertisements are there?
MCQ
3495
If, for a Poisson distributed random variable X\displaystyle X, the probability for X\displaystyle X taking value 2 is 3 times the probability for X\displaystyle X taking value 4, then the variance of X\displaystyle X is
MCQ
3496
The manufacturer of a certain electronic component is certain that 2%\displaystyle 2\% of his product is defective. He sells the components in boxes of 120 and guarantees that not more than 2%\displaystyle 2\% in any box will be defective. Find the probability that a box selected at random would fail to meet the guarantee? (e−2.4=0.0907\displaystyle e^{-2.4} = 0.0907)
MCQ
3497
A renowned hospital usually admits 200 patients everyday. One percent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?
MCQ
3498
If Standard Deviation is 1.732 then what is the value of poisson distribution. The P(−2.48<X<3.54)\displaystyle P(-2.48 < X < 3.54) is
MCQ
3499
If a Poisson distribution is such that P(X=2)=P(X=3)\displaystyle P(X=2) = P(X=3) then the variance of the distribution
MCQ
3500
Between 9 AM and 10 AM, the average number of phone calls per minute coming into the switchboard of a company is 4. Find the probability that in one particular minute there will be either 2 phone calls or no phone calls (given e−4=0.018316\displaystyle e^{-4} = 0.018316)
MCQ
3502
The mean of Poisson distribution is 4. The probability of two-successes is____.
MCQ
3511
In Poisson distribution which of them is same.
MCQ
3512
Number of defects in clothes a garments showroom will form a
MCQ
3513
In a certain Poisson frequency distribution, the probability corresponding to two success is half the probability corresponding to three successes. The mean of the distribution is
MCQ
3514
Which one is not a condition of Poisson model
MCQ
3515
In ______ distribution, mean = variance.
MCQ
3516
For a Poisson variate X, P(X=1)=P(X=2)\displaystyle P(X=1) = P(X=2). What is the mean of X?
MCQ
3519
For a Poisson variate X, P(X=2)=3P(X=4)\displaystyle P(X=2) = 3 P(X=4). Then the standard deviation of X is
MCQ
3520
If X be a Poisson variates with parameter λ\displaystyle \lambda, then find P(3<X<5)\displaystyle P(3 < X < 5) (Given e−0.36783=0.6923\displaystyle e^{-0.36783} = 0.6923)
MCQ
3521
In a Poisson Distribution P(X=0)=P(X=2)\displaystyle P(X=0) = P(X=2). Find E(X)\displaystyle E(X)
MCQ
3522
Name of the distribution which has Mean=Variance
MCQ
3523
If 5%\displaystyle 5\% of the electric bulbs manufactured by a company are defective, use Poisson distribution to find the probability that in a sample of 100\displaystyle 100 bulbs, 5\displaystyle 5 bulbs will be defective. [Given : e−5=0.007\displaystyle e^{-5} = 0.007 ]
MCQ
3524
For a Poisson variate X, P(X=1)=P(X=2)\displaystyle P(X=1) = P(X=2), what is the mean of X?
MCQ
3525
In a Poisson distribution if P(X=4)=P(X=5)\displaystyle P(X=4) = P(X=5) then the parameter of Poisson distribution is:
MCQ
3526
If Poisson distribution is such that P(X=2)=P(X=3)\displaystyle P(X=2) = P(X=3) then the Standard Deviation of the distribution is
MCQ
3527
To find the distribution of number of airplanes crashing every hour in the world, which of the following distribution is appropriate to apply:
MCQ
3529
For the Poisson distribution:
MCQ
3530
Which of the following is uni-parametric distribution
MCQ
3974
For a Poisson variate X, P(X=1)=P(X=2)\displaystyle P(X=1) = P(X=2), what is the mean of X?
MCQ
3534
In a Poisson distribution if P(X=4)=P(X=5)\displaystyle P(X=4) = P(X=5) then the parameter of Poisson distribution is:
MCQ
3975
If Poisson distribution is such that P(X=2)=P(X=3)\displaystyle P(X=2) = P(X=3) then the Standard Deviation of the distribution is
MCQ
3569
The mean deviation about median of a standard normal variate is
MCQ
3976
To find the distribution of number of airplanes crashing every hour in the world, which of the following distribution is appropriate to apply:
MCQ
3977
The mean and variance are equal for which of the following:
MCQ
3978
For the Poisson distribution:
MCQ
3979
Which of the following is uni-parametric distribution
MCQ
3531
The probability that a man aged 45\displaystyle 45 years will die within a year is 0.012\displaystyle 0.012. What is the probability that of 10\displaystyle 10 men, at least 9\displaystyle 9 will reach their 46\displaystyle 46th birthday? [Given e−0.12=0.88692\displaystyle e^{-0.12} = 0.88692 ]
MCQ
3532
In a certain manufacturing process, 5%\displaystyle 5\% of the tools produced turn out to be defective. Find the probability that in a sample of 40\displaystyle 40 tools, at most 2\displaystyle 2 will be defective: Given e−2=0.135\displaystyle e^{-2} = 0.135
MCQ
3533
If standard deviation of a Poisson distribution is 2\displaystyle 2, then its Mode
MCQ
3980
In Poisson distribution if P(X=4)=P(X=5)\displaystyle P(X=4) = P(X=5) then the parameter of Poisson distribution is:
MCQ
3535
In _________ distribution, mean = variance.
MCQ
3536
The mean of Poisson distribution is 4\displaystyle 4. The probability of two-successes in
MCQ
3588
An example of a bi-parametric continuous probability distribution
MCQ
3539
If for a normal distribution Q1=54.52\displaystyle Q_1 = 54.52 and Q3=78.86\displaystyle Q_3 = 78.86, then the median of the distribution is
MCQ
3540
What is the mean of X having the following density function? f(x)=14π2e−(x−10)232\displaystyle f(x) = \frac{1}{\sqrt{4\pi}2} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3541
Area between −1.96\displaystyle -1.96 to +1.96\displaystyle +1.96 in a normal distribution is:
MCQ
3542
If the points of inflexion of a normal curve are 40\displaystyle 40 & 60\displaystyle 60 respectively, then mean deviation is:
MCQ
3543
Area under ±3σ\displaystyle \pm 3\sigma
MCQ
3544
What is the mean and SD if f(x)=12πe−(x−3)22\displaystyle f(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{(x-3)^2}{2}}, −∞<x<∞\displaystyle -\infty < x < \infty.
MCQ
3545
If we change the parameter(s) of a distribution the shape of probability curve does not change.
MCQ
3546
The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is
MCQ
3547
For a normal distribution, the value of third moment about mean is.
MCQ
3548
In normal distribution, Mean, Median and Mode are:
MCQ
3549
For a certain type of mobile, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. A person owns one of these mobiles and want to know the probability that the length of time will be between 50 and 70 hours is (given q(1.33)=0.9082,q(0)=0.5\displaystyle q(1.33) = 0.9082, q(0) = 0.5)?
MCQ
3550
Let x\displaystyle x be normal distribution with mean 2.5 and variance 1. If P(x≤2.5)=0.4772\displaystyle P(x \le 2.5) = 0.4772 and that the cumulative normal probability value at 2 is 0.9772, then a=?\displaystyle a = ?
MCQ
3551
In a normal distribution, variance is 16 then the value of mean deviation is.
MCQ
3552
Skewness of Normal Distribution is:
MCQ
3553
The speeds of a number of bikes follow a normal distribution model with a mean of 83 km/hr and a standard deviation of 9.4 km/hr. Find the probability that a bike picked at random is travelling at more than 95km/hr.? Given P(Z>1.28)=0.1003\displaystyle P(Z > 1.28) = 0.1003
MCQ
3554
In a Standard Normal distribution, then the value of the mean(μ\displaystyle \mu) and SD (σ\displaystyle \sigma) is:
MCQ
3555
If 'x' and 'y' are independent normal variate with mean and SD μ1,μ2\displaystyle \mu_1, \mu_2 and σ1,σ2\displaystyle \sigma_1, \sigma_2 respectively, then for z=x+y\displaystyle z = x + y which also follows normal distribution mean and SD are:
MCQ
3556
For a normal distribution, the ratio of mean deviation to the standard deviation is _____
MCQ
3557
In a class of 100 students, the mean marks was 50 with Standard Deviation 14.9. Assuming the distribution of marks to be normal, find the number of students who obtained more than 70% marks (at Z=1.34\displaystyle Z = 1.34, area =0.4099\displaystyle = 0.4099).
MCQ
3558
Quartile deviation of a normal distribution with Mean of 10 and SD of 4 is:
MCQ
3559
If X and Y are 2 independent normal variables with mean as 10 and 12 and Standard Deviation (S.D) as 3 and 4 respectively, then (X+Y)\displaystyle (X + Y) is normally distributed with:
MCQ
3561
In a normal distribution skewness is _____
MCQ
3562
The points of inflexion of the normal curve f(t)=142πe−(t−32)232\displaystyle f(t) = \frac{1}{4\sqrt{2\pi}} e^{-\frac{(t-32)^2}{32}} are
MCQ
3564
If X is normal variate with mean 6 and variance 16 then the value of the probability. P(2≤X≤10)\displaystyle P(2 \le X \le 10) is equal to.
MCQ
3565
The total area of the normal curve is
MCQ
3566
If the mean deviation of a normal variable is 16, what is its quartile deviation?
MCQ
3570
If the points of inflexion of a normal curve are 40 & 60 respectively, then its mean deviation
MCQ
3568
For Poisson fitting to an observed frequency distribution
MCQ
3571
What is the first quartile of X having the following probability density function? f(t)=142πe−(t−10)232\displaystyle f(t) = \frac{1}{4\sqrt{2\pi}} e^{-\frac{(t-10)^2}{32}} for −∞<X<∞\displaystyle -\infty < X < \infty
MCQ
3584
What is the mean of X having the following density function f(x)=142πe−(x−10)232\displaystyle f(x) = \frac{1}{4\sqrt{2\pi}} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3585
What is the first quartile of X having the following probability density function? F(x)=12πe−(x−10)232\displaystyle F(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3586
If X follows normal distribution with μ=50\displaystyle \mu = 50 and σ=10\displaystyle \sigma = 10, what is value of P(X≤60∣X>50)\displaystyle P(X \le 60 | X > 50)?
MCQ
3587
For a normal distribution with mean as 500 and SD as 120, what is the value of k so that the interval [500, k] covers 40.32 per cent area of the normal curve? (Given ϕ(1.30)=0.9032\displaystyle \phi(1.30) = 0.9032)
MCQ
3589
What is the mean of X having the following density function? f(x)=142πe−(x−10)232\displaystyle f(x) = \frac{1}{4\sqrt{2\pi}} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3590
The variance of standard normal distribution
MCQ
3591
For a normal distribution, the first and third quartile are given to be 37 and 49, the mode of the distribution is.
MCQ
3592
Area between -1.96 to +1.96 in a normal distribution is :
MCQ
3593
The speeds of bikes follow a normal distribution model with a mean of 80\displaystyle 80 km/hr. and a standard deviation of 9.4\displaystyle 9.4 km/hr. Find the probability that a bike picked at random is travelling at more than 95\displaystyle 95 km/hr.? [P(z)=P(1.60)=0.4452]\displaystyle [P(z) = P(1.60) = 0.4452]
MCQ
3583
For a normal distribution Q1=54.32\displaystyle Q_1 = 54.32 and Q3=78.86\displaystyle Q_3 = 78.86, then the median of the distribution is
MCQ
3989
For a normal distribution, the first and third quartile are given to be 37 and 49, the mode of the distribution is.
MCQ
3983
What is the first quartile of X having the following probability density function? F(x)=12πe−(x−10)232\displaystyle F(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3985
For a normal distribution with mean as 500 and SD as 120, what is the value of k so that the interval [500, k] covers 40.32 per cent area of the normal curve? (Given ϕ(1.30)=0.9032\displaystyle \phi(1.30) = 0.9032)
MCQ
3986
An example of a bi-parametric continuous probability distribution
MCQ
3987
What is the mean of X having the following density function? f(x)=142πe−(x−10)232\displaystyle f(x) = \frac{1}{4\sqrt{2\pi}} e^{-\frac{(x-10)^2}{32}} for −∞<x<∞\displaystyle -\infty < x < \infty
MCQ
3988
The variance of standard normal distribution
MCQ
3991
The speeds of bikes follow a normal distribution model with a mean of 80\displaystyle 80 km/hr. and a standard deviation of 9.4\displaystyle 9.4 km/hr. Find the probability that a bike picked at random is travelling at more than 95\displaystyle 95 km/hr.? [P(z)=P(1.60)=0.4452]\displaystyle [P(z) = P(1.60) = 0.4452]
MCQ
3594
Which of the following is not a property of normal distribution?
MCQ
3595
For a continuous random variable following standard normal distribution, what is the value of standard deviation?
MCQ
3596
If the inflexion points of a normal distribution are 6\displaystyle 6 and 14\displaystyle 14. Find its SD
MCQ
3597
Normal distribution is also known as
MCQ
3993
If the inflexion points of a normal distribution are 6\displaystyle 6 and 14\displaystyle 14. Find its SD
MCQ
3994
Normal distribution is also known as
MCQ
3610
The mean deviation about median of standard normal variate is
MCQ
3995
If the Quartile Deviation of a normal distribution with mean 10\displaystyle 10 and SD 4\displaystyle 4 is
MCQ
3996
If the two Quartiles N(μ,σ2)\displaystyle N(\mu, \sigma^2) are 14.6\displaystyle 14.6 and 25.4\displaystyle 25.4 respectively. What is the standard deviation of the distribution?
MCQ
3997
The wages of workers of a factory follows
MCQ
3998
If the inflexion points of a Normal Distribution are 6\displaystyle 6 and 14\displaystyle 14. Find its SD?
MCQ
3603
An approximate relation between quartile deviation (QD) and standard deviation (S.D.) of normal distribution is:
MCQ
3604
Which of the following is not a characteristic of a normal probability distribution?
MCQ
3605
The Interval (μ−3σ,μ+3σ)\displaystyle (\mu - 3\sigma, \mu + 3\sigma) covers
MCQ
3606
If the mean deviation of a normal variable is 16\displaystyle 16, what is its quartile deviation?
MCQ

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