Question

The prices of all houses in New York State have a probability distribution that is skewed to the right with a mean of $157,000 and a standard deviation of $29,500. Let

xbar be the mean of price of a sample of 400 houses selected from New York State.What is the probability that the mean price obtained from this sample will be within $3000 of the population mean?

Answer 1

Given,

= 157000, = 29500 , n = 400

Sample size is sufficiently large, so we use central limit theorem.

P( < x) = P( Z < x - / ( / sqrt(n) ) )

We have to calculate P( - 3000 < < + 3000) = ?

That is

P(157000 - 3000 < < 157000 + 3000) = ?

P( 154000 < < 160000) = ?

P( 154000 < < 160000) = P( < 160000) - P( < 154000)

= P( Z < 160000 - 157000 / 29500 / sqrt(400) ) - P( Z < 154000 - 157000 / 29500 / sqrt(400) )

= P( Z < 2.0339) - P (Z < -2.0339)

= P( Z < 2.0339) - ( 1 - P( Z < 2.0339) )

= 0.9790 - ( 1 - 0.9790)

= 0.9580