Question

The sales price of a single family house in Charlotte is normally distributed with mean $210,000 and standard deviation $35,000. 1. A random sample of 49 single-family houses in Charlotte is selected. Let X ¯ be the mean sales price of the sample. What is the mean of X ¯?

Answer 1

E(X ¯)=210,000.

Explanation:

A sampling distribution for samples of size n=49 from a population with means μ=210,000 and standard deviation σ=35,000, has the following means anda standard deviation:

`\mu_s=\mu=210,000\\\\\sigma_s=\sigma/√(n)=35,000/√(49)=35,000/7=5,000`

If X ¯ is the mean sales price of the sample, it will have a mean value of E(X ¯)=210,000.