Question

A report announced that the mean sales price of all new houses sold one year was $272,000. Assume that the population standard deviation of the prices is $100,000. If you select a random sample of 100 new houses, what is the probability that the sample mean sales price will be between $250,000 and $285,000?

Select one:

a. 0.8893

b. 0.8034

c. 0.2956

d. 0.1388

Answer 1

Solution :

Given that,

mean = = $272000

standard deviation = = $100000

= / n = 100000 / 100 = 10000

= P[(250000 - 272000) /10000 < ( - ) / < (285000 - 272000) /10000 )]

= P(-2.2 < Z < 1.3)

= P(Z < 1.3) - P(Z < -2.2)

= 0.9032 - 0.0139 = 0.8893

Probability = 0.8893

Option a is