Question

13. The Arizona Regional Multiple Listing Service publishes several books for the real-estate industry. One such book deals with the region termed "Residential South-west," composed of Mesa, Temp, and Chandler, Arizona. This book indicates that the mean sale price of homes in that region is $277,500 with a standard deviation of $21,500. Suppose you take a sample of 250 homes from the area. a. Describe the distribution of the sample mean symbolically. (4 points) b. What is the probability the mean home cost would be greater than $282,500? (6 points)

Answer 1

Solution :

Given that,

mean = $\mu$ = 277500

standard deviation = $\sigma$ = 21500

n = 250

$\mu$
_T
= 277500

$\sigma$
_T
= $\sigma$ / $\sqrt$ n = 21500 / $\sqrt$ 250 = 1359.7794

a) The distribution of the sample mean  $\mu$
_T
= 277500

The standard deviation of the sample mean $\sigma$
_T
= 1359.7794

b) P(
T
> 282500 ) = 1 - P(
T
< 282500)

= 1 - P[(
T
- $\mu$
_T
) / $\sigma$
_T
< ( 282500 - 277500) / 1359.7794 ]

= 1 - P(z < 3.677)

Using z table,    

= 1 - 0.9999

= 0.0001

Probability = 0.0001