**Exercise 07.54 Algorithm (Sampling Distribution of x)****Problem Statement:**After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $29,200. Assume the population standard deviation is $6,600. Suppose that a random sample of 80 USC students will be taken from this population. Use the z-table to solve the following:**a. What is the value of the standard error of the mean?**- Answer: 738 (to nearest whole number)**b. What is the probability that the sample mean will be more than $29,200?**- Answer: [Space provided for answer] (to 2 decimals)**c. What is the probability that the sample mean will be within $1,250 of the population mean?**- Answer: [Space provided for answer] (to 4 decimals)**d. How would the probability in part (c) change if the sample size were increased to 180?**- Answer: [Space provided for answer] (to 4 decimals)**Feedback:**- Partially Correct**Instructions:**Use the information provided alongside statistical methods to determine the solution to each part. For part (a), calculate the standard error using the formula:\[ SE = \frac{\sigma}{\sqrt{n}} \]For parts (b) and (c), utilize the z-table to determine the probabilities required. Consider how changing the sample size in part (d) affects the standard error and consequently the probabilities.**Note:** No diagrams or graphs are included in the image.

Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $29,200. Assume the population standard deviation is $6,600. Suppose that a random sample of 80 uSC students will be taken from this population. Use z-table. a. What is the value of the standard error of the mean? 738 (to nearest whole number) b. What is the probability that the sample mean will be more than $29,200? (to 2 decimals) c. What is the probability that the sample mean will be within $1,250 of the population mean? (to 4 decimals) d. How would the probability in part (c) change if the sample size were increased to 180? (to 4 decimals)

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $29,200. Assume the population standard deviation is $6,600. Suppose that a random sample of 80 uSC students will be taken from this population. Use z-table. a. What is the value of the standard error of the mean? 738 (to nearest whole number) b. What is the probability that the sample mean will be more than $29,200? (to 2 decimals) c. What is the probability that the sample mean will be within $1,250 of the population mean? (to 4 decimals) d. How would the probability in part (c) change if the sample size were increased to 180? (to 4 decimals)

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Exercise 07.54 Algorithm (Sampling Distribution of x)**

**Problem Statement:**

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $29,200. Assume the population standard deviation is $6,600. Suppose that a random sample of 80 USC students will be taken from this population. Use the z-table to solve the following:

**a. What is the value of the standard error of the mean?**

- Answer: 738 (to nearest whole number)

**b. What is the probability that the sample mean will be more than $29,200?**

- Answer: [Space provided for answer] (to 2 decimals)

**c. What is the probability that the sample mean will be within $1,250 of the population mean?**

- Answer: [Space provided for answer] (to 4 decimals)

**d. How would the probability in part (c) change if the sample size were increased to 180?**

- Answer: [Space provided for answer] (to 4 decimals)

**Feedback:**

- Partially Correct

**Instructions:**

Use the information provided alongside statistical methods to determine the solution to each part. For part (a), calculate the standard error using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} \]

For parts (b) and (c), utilize the z-table to determine the probabilities required. Consider how changing the sample size in part (d) affects the standard error and consequently the probabilities.

**Note:** No diagrams or graphs are included in the image.

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