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Sketch the sampling distribution of xand calculate the probability that the sample mean will be greater than 193 mg/dl.

Sketch the sampling distribution of xand calculate the probability that the sample mean will be greater than 193 mg/dl.

MATLAB: An Introduction with Applications
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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When the population is Normally distributed, we know that the sampling distribution of xwill be Normally distributed, so we can use Normal calculations. However, most population distributions are not Normally distributed. If our sampling distribution is skewed, non-Normal in some other way, or totally unknown, we cannot use Normal calculations to answer questions. Thankfully, a pretty remarkable fact about sample means helps us out: The Central Limit Theorem (CLT). When the sample size is large, the shape of the sampling distribution of xwill be approximately Normal no matter what the shape of the population distribution may be! The AP Statistics people define "large" to be any sample thatts at least 30. So, if n 230, we can be safe in assuming that the sampling distribution of x will be approximately Normal and we can proceed to perform Normal calculations. If n < 30, we can only proceed if we know the population distribution is Normal. The blood cholesterol level of adult men has mean 188 mg/dhand standard deviation 41mg/dl. An SRS of 250 men is selected and the mean blood cholesterol level in the sample is calculated. Sketch the sampling distribution of xand calculate the probability that the sample mean will be greater than 193 mg/dl.
Transcribed Image Text:When the population is Normally distributed, we know that the sampling distribution of xwill be Normally distributed, so we can use Normal calculations. However, most population distributions are not Normally distributed. If our sampling distribution is skewed, non-Normal in some other way, or totally unknown, we cannot use Normal calculations to answer questions. Thankfully, a pretty remarkable fact about sample means helps us out: The Central Limit Theorem (CLT). When the sample size is large, the shape of the sampling distribution of xwill be approximately Normal no matter what the shape of the population distribution may be! The AP Statistics people define "large" to be any sample thatts at least 30. So, if n 230, we can be safe in assuming that the sampling distribution of x will be approximately Normal and we can proceed to perform Normal calculations. If n < 30, we can only proceed if we know the population distribution is Normal. The blood cholesterol level of adult men has mean 188 mg/dhand standard deviation 41mg/dl. An SRS of 250 men is selected and the mean blood cholesterol level in the sample is calculated. Sketch the sampling distribution of xand calculate the probability that the sample mean will be greater than 193 mg/dl.
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