A report announced that the median sales price of new houses sold one year was $

Question

A report announced that the median sales price of new houses sold one year was $231,000, and the mean sales price was $274,300. Assume that the standard deviation of the prices is $80,000.

The probability that the sample mean will be less than $300,000 is .9993.

The probability that the sample mean will be be between $275,000 and $295,000 is _________.

(Round to four decimal places as needed.)

a.) If you select a random sample of n=100, what is the probability that the sample mean will be less than $300,000?

Explanation / Answer

Ans:

standard errror of mean=80000/sqrt(100)=8000

a)

z=(300000-274300)/8000=3.21

P(z<3.21)=0.9993

b)

zl=(275000-274300)/8000=0.0875

zu=(295000-274300)/8000=2.5875

P(0.0875<=z<=2.5875)=P(z<=2.5875)-P(z<=0.0875)

=0.9952-0.5349

=0.4603

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