Question

A sample of size 35 is drawn from a population that has a mean of 17 and a standard deviation of 3.7, and the population is not normally distributed. Give your answers to two decimal places. a. (2 pts) What is the mean of the sample means (show your work)? b. (3 pts) What is the standard deviation of the sample means (show your work)? c. (2 pt) Is it true the Central Limit Theorem can be applied, and the shape of the sample means is approximately normal? Circle one: YES NO

Answer #1

Solution :

Given that,

mean = = 17

standard deviation = = 3.7

n = 35

a)

The mean of the sample means is,

_{}
= 17 and

b)

the standard deviation of the sample means

_{}
=
/
n = 3.7 /
35 = 06254

c)

Yes it's true .

the Central Limit Theorem can be applied, and the shape of the sample means is approximately normal .

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