Question

The average sales price of a single-family house in the United states is $235,500. You randomly select 12 single-family houses. What is the probability that the mean sales price is more than $225,000? Assume that the sales prices are normally distributed with a standard deviation of $50,000?

Answer 1

Given

= 235500

=50000

n=11

Now calculate probability that mean sales prize is more than 225000.

P(x> 225000) = 0.5 + p(0< Z < x-/(/n))

= 0.5 + p( 0< Z < 225000-235500/(50000/12))

= 0.5 + p( 0< Z < - 0.73)

= 0.5 + 0.2673

P(x> 225000) = 0.7673

Probability that the Mean sales price is more than 225000 is 0.7673.