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.

• Find the mean of the sampling distribution
• Find the standard error of the sampling distribution.
• What is the probability that this sample mean will be between 40 and 50?

Answer 1

Mean of sampling distribution = 45

Standard error $=\frac{\sigma}{\sqrt{n}}=\frac{10}{\sqrt{36}}=1.67$

Probability between 40 and 50

$P(40<x<50)=P(\frac{40-45}{\frac{10}{\sqrt{36}}}<Z<\frac{50-45}{\frac{10}{\sqrt{36}}})$

$=P(-3<Z<3)=P(Z<3)-P(Z<-3)$

$=0.9987-0.0013=0.9974$