**Central Limit Theorem and Sampling Distribution**A population of values has a distribution with a mean (\(\mu\)) of 50.1 and a standard deviation (\(\sigma\)) of 71.2. You intend to draw a random sample of size \(n = 96\).According to the Central Limit Theorem:1. **Mean of the Distribution of Sample Means** (a) What is the mean of the distribution of sample means? \[ \mu_{\bar{x}} = \quad \_\_\_\_\_ \]2. **Standard Deviation of the Distribution of Sample Means** (b) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) \[ \sigma_{\bar{x}} = \quad \_\_\_\_\_ \]3. **Probability of Sample Mean Being More Than 45** (c) In a random sample of \(n=96\), what is the probability that its sample mean is more than 45? Round to three decimal places. \[ \_\_\_\_\_ \]4. **Probability of Sample Mean Being Less Than 73.5** (d) In a random sample of \(n=96\), what is the probability that its sample mean is less than 73.5? Give your answer to three decimal places. \[ \_\_\_\_\_ \]To solve these problems, apply the properties defined by the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large (typically \(n \geq 30\)), regardless of the shape of the population distribution.

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A population of values has a distribution with u = 50.1 and o = 71.2. You intend to draw a random sample of size n = 96. According to the Central Limit Theorem: (a) What is the mean of the distribution of sample means? (b) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) (c) In a random sample of n=96, what is the probability that its sample mean is more than 45? Round to three decimal places. (d) In a random sample of n=96, what is the probability that its sample mean is less than 73.5? Give your answer to three decimal places.

A population of values has a distribution with u = 50.1 and o = 71.2. You intend to draw a random sample of size n = 96. According to the Central Limit Theorem: (a) What is the mean of the distribution of sample means? (b) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) (c) In a random sample of n=96, what is the probability that its sample mean is more than 45? Round to three decimal places. (d) In a random sample of n=96, what is the probability that its sample mean is less than 73.5? Give your answer to three decimal places.

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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