**Topic: Statistical Analysis of Minority Representation in Hiring**A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly 10% of all applications were from minority members, and exactly 8% of the 900 open positions were filled by members of the minority.**Answer the following:**(If necessary, consult a [list of formulas](#)).**(a)** Find the mean of $ \hat{P} $, where $ \hat{P} $ is the proportion of minority member applications in a random sample of 900 that is drawn from all applications.\[ \boxed{} \]**(b)** Find the standard deviation of $ \hat{P} $.\[ \boxed{} \]**(c)** Compute an approximation for $ P(\hat{p} \leq 0.08) $, which is the probability that there will be 8% or fewer minority member applications in a random sample of 900 drawn from all applications. Round your answer to four decimal places.\[ \boxed{} \][Continue]**Explanation of Formulas and Results:**1. **Mean of $ \hat{P} $**: - The mean $ \mu_{\hat{P}} $ of the sample proportion $ \hat{P} $ can be found using the formula: \[ \mu_{\hat{P}} = p \] where $ p $ is the true proportion of all minority member applications. 2. **Standard Deviation of $ \hat{P} $**: - The standard deviation $ \sigma_{\hat{P}} $ of the sample proportion $ \hat{P} $ is calculated using: \[ \sigma_{\hat{P}} = \sqrt{\frac{p(1 - p)}{n}} \] where $ p $ is the true proportion of minority applications and $ n $ is the sample size.3. **Approximation for Probability $ P(\hat{p} \leq 0.08) $**: - To approximate the probability that the sample proportion $ \hat{P} $ is less than or equal to 0.08, we can use the normal distribution as an approximation to the binomial distribution: \[ Z = \frac{\hat{p} - \mu_{\hat{P}}

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A minority representation group accuses a major bank of racial discrimination in its recent hires for financia from minority members, and exactly 8% of the 900 open positions were filled by members of the minority.

A minority representation group accuses a major bank of racial discrimination in its recent hires for financia from minority members, and exactly 8% of the 900 open positions were filled by members of the minority.

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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