Z SCORE QUESTION

Question

The mean price of new homes from a sample of housed is $155,000, with a standard deviation of $15,000. Calculate the z-scores to determine if the following house prices are unusual. (Write yes or no to the right of the z-score)

(a) $200, 000

(b) $55,000

(c) $175,000

(d) $122,000

Answer 1

The z-score would be calculated using z=(x-mu)/sigma.

 

(a)  = (200000-155000)/15000 = 3.0 .

 

If you use a .05 alpha level the critical z values are +-1.96 so (a) would be yes.

 

The others are done in a similar manner.

 

 

Any questions comment back.

Answer 2

(a) z-score is (200,000 - 155,000) / 15,000 = 3    (highly unusual - in the top 0.002)

 

(b) z-score is (55,000 - 155,000) / 15,000 = -6.667 (highly unusual - in the bottom 0.00001) very, very small I do not even know how small

 

(c) z-score is (175,000 - 155,000) / 15,000 = 1.33 (fairly normal (in the top 0.30)

 

(d) z-score is (122,000 - 155,000) / 15,000 = -2.2 (highly unusally in the bottom 0.02)