### Example Problem: Probability in Normal Distribution#### Problem:The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed with:- Mean (μ) = 34 minutes - Standard deviation (σ) = 7 minutes. **Question**: What is the probability that the average length of time for nine interviews will be 40 minutes or longer?#### Solution Steps:1. **Identify the given variables**: - Mean (μ) = 34 minutes - Standard deviation (σ) = 7 minutes - Sample size (n) = 92. **Calculate the standard error of the mean (SEM)** using the formula: \[ SEM = \frac{\sigma}{\sqrt{n}} \]3. **Plug in the values**: \[ SEM = \frac{7}{\sqrt{9}} = \frac{7}{3} \approx 2.33 \]4. **Calculate the Z-score** to find the probability using the Z-formula: \[ Z = \frac{X - \mu}{SEM} \] where X is the desired average time (40 minutes in this case).5. **Plug in the values**: \[ Z = \frac{40 - 34}{2.33} \approx \frac{6}{2.33} \approx 2.58 \]6. **Find the probability** from the Z-table corresponding to the calculated Z-score (2.58).7. From the Z-table, a Z-score of 2.58 has a cumulative probability of about 0.9951. 8. **Calculate the probability of the average interview time being 40 minutes or longer**: Since we need 40 minutes or longer, \[ P(X \ge 40) = 1 - P(X < 40) = 1 - 0.9951 = 0.0049 \]#### Answer:The probability that the average length of time for nine interviews will be 40 minutes or longer is approximately 0.0049, or 0.49%.

Given that mean = 34 ,s.d =7 ,n =9

Answered: MAK 1. The personal office at a large…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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