A normal distribution has μ = 368 and σ = 42.When samples of n = 36 are taken:What is the expected value of the mean and standard error for the distribution of sample means?What is the probability of getting a sample mean greater than 355?What is the probability of getting a sample mean less than 377?What is the probability of getting a sample mean greater than 385?

Answered: A normal distribution has μ = 368 and σ…

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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Question

A normal distribution has μ = 368 and σ = 42.When samples of n = 36 are taken:
What is the expected value of the mean and standard error for the distribution of sample means?
What is the probability of getting a sample mean greater than 355?
What is the probability of getting a sample mean less than 377?
What is the probability of getting a sample mean greater than 385?

Expert Solution

Step 1

A normal distribution follows a bell shaped curve which is centred at the mean and it is also called Gaussian distribution. The normal distribution with 0 mean and 1 standard deviation is called standard normal distribution.

According to central limit theorem if the population is normal or the sample size is at lest 30, then the sampling distribution of sample mean also follows the normal distribution. The mean of sampling distribution is equal to population mean and the standard deviation (also called standard error) is computed by $\frac{σ}{\sqrt{n}}$ .