Theoretical DistributionsMCQMTP June 2023 Series IQuestion 3593 of 230
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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]

Options

A0.0548\displaystyle 0.0548
B0.38\displaystyle 0.38
C0.49\displaystyle 0.49
D0.278\displaystyle 0.278
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Correct Answer

Option a0.0548\displaystyle 0.0548

All Options:

  • A0.0548\displaystyle 0.0548
  • B0.38\displaystyle 0.38
  • C0.49\displaystyle 0.49
  • D0.278\displaystyle 0.278

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Detailed Solution & Explanation

**Probability for Bike Speeds (Normal Distribution)** We are given: - Mean speed μ=80\displaystyle \mu = 80 km/hr - Standard deviation σ=9.4\displaystyle \sigma = 9.4 km/hr We want to find the probability that a bike speed X\displaystyle X is greater than 95\displaystyle 95 km/hr: P(X>95)P(X > 95) **Step 1: Standardize the value X=95\displaystyle X = 95** Z=Xμσ=95809.4=159.41.59571.60Z = \frac{X - \mu}{\sigma} = \frac{95 - 80}{9.4} = \frac{15}{9.4} \approx 1.5957 \approx 1.60 **Step 2: Calculate the probability P(Z>1.60)\displaystyle P(Z > 1.60)** Using the symmetry of the standard normal curve: - The total area to the right of the mean Z=0\displaystyle Z = 0 is 0.5000\displaystyle 0.5000. - The area from Z=0\displaystyle Z = 0 to Z=1.60\displaystyle Z = 1.60 is given as P(0Z1.60)=0.4452\displaystyle P(0 \le Z \le 1.60) = 0.4452. Therefore: P(Z>1.60)=0.5000P(0Z1.60)P(Z > 1.60) = 0.5000 - P(0 \le Z \le 1.60) P(Z>1.60)=0.50000.4452=0.0548P(Z > 1.60) = 0.5000 - 0.4452 = 0.0548 This matches Option A. 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

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