Question

A sample size of 15 is drawn from a population with a mean of 100 standard deviation of 28 is it appropriate to use the normal distribution to find probabilities of the sample mean

Answer 1

It is easy to find the probabilities for a sample mean if it has a normal distribution. You can find probabilities if the sample size, n, is large enough.

The normal distribution is a very simple distribution that has a table (see z table at the end of solution) for finding probabilities and anything else you need.

You can find probabilities for

by converting the

to a z-value and finding probabilities using the Z-table (see below).

The general conversion formula :

We will substitute the appropriate values of the mean and standard error of :

the conversion formula is :

the z-table is :

P.S. (please upvote if you find the answer satisfactory)