### Probability and Statistics Exercise**Objective:** Determine probabilities and interpret results regarding sample means.#### Tasks:1. **Find the Probability:** - **Question:** What is the probability that the sample mean is less than $68,680? - **Notation:** P( Suppose the mean starting salary for nurses is $67,290 nationally. The standard deviation is approximately $10,478. The starting salary is not normally distributed, but it is mound shaped. A sample of 45 starting salaries for nurses is taken.**State the random variable:**- The mean starting salary of a nurse.- Starting salary for a nurse.- The standard deviation of starting salaries of nurses.The correct choice is: - The mean starting salary of a nurse.**What is the mean of the distribution of all sample means?**\[ \mu_{\bar{x}} = \]**What is the standard deviation of the distribution of all sample means? Round to five decimal places.**\[ \sigma_{\bar{x}} = \]**What is the shape of the sampling distribution of the sample mean? Why?**- You can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30. - You can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30. - You can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.The correct choice is:- You can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30.

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Answered: Suppose the mean starting salary for…

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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Suppose the mean starting salary for nurses is $67,290 nationally. The standard deviation is approximately $10,478. The starting salary is not normally distributed but it is mound shaped. A sample of 45 starting salaries for nurses is taken.