Question

A sample size of 36 is to be selected from a population that has a mean of µ = 45 and standard deviation s of 10.

1.Find the mean of the sampling distribution

2.Find the standard error of the sampling distribution.

3.What is the probability that this sample mean will be between 40 and 50?

Answer 1

a. $\mu=45$

b.$\sigma_x=\sigma/\sqrt{n}=10/6=1.7$

$SE=\frac{\sigma}{\sqrt{n}}=10/\sqrt{36}=1.7$

c.

$P(40<X<50)=P(\frac{40-45}{1.7}<X<\frac{50-45}{1.7})=P(-2.94<X<2.94)=0.99836-0.00164=0.99162$