Theoretical DistributionsMCQPYQ Dec 23Question 3553 of 230
All Questions

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

Options

A0.1003
B0.38
C0.49
D0.278
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 0.1003

All Options:

  • A0.1003
  • B0.38
  • C0.49
  • D0.278

Ad

Detailed Solution & Explanation

**Probability Calculation for Normally Distributed Speed** Let X\displaystyle X represent the speed of a randomly selected bike (in km/hr). Given: - X∼N(μ,σ2)\displaystyle X \sim N(\mu, \sigma^2) where μ=83\displaystyle \mu = 83 and σ=9.4\displaystyle \sigma = 9.4 We want to find the probability that a bike travels at more than 95\displaystyle 95 km/hr: P(X>95)P(X > 95) **Step 1: Standardize the limit using the Z-score formula** Z=X−μσZ = \frac{X - \mu}{\sigma} For X=95\displaystyle X = 95: Z=95−839.4=129.4≈1.2766≈1.28Z = \frac{95 - 83}{9.4} = \frac{12}{9.4} \approx 1.2766 \approx 1.28 **Step 2: Calculate the probability** P(X>95)=P(Z>1.28)P(X > 95) = P(Z > 1.28) We are given the standard normal cumulative probability: P(Z>1.28)=0.1003P(Z > 1.28) = 0.1003 Therefore, the probability that a randomly picked bike is travelling at more than 95\displaystyle 95 km/hr is 0.1003\displaystyle 0.1003. Hence, **Option A** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

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.

View Official ICAI Syllabus

Exam Strategy Tip

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

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

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

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

Ready to Master Theoretical Distributions?

Practice all 230 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free