Question

The U.S. Census Bureau announced that the median sales price of new house sold in December of 2018 $322,800, and the mean sales price was $376,000 (https://www.census.gov/construction /nrs/pdf/uspricemon.pdf). Assume that the standard deviation of the prices is $90,000.

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

b. If you select a random sample of n = 100, what is the probability that the sample mean will be between $275,000 and $290,000

Answer 1

a) According to the central limit theorem, the distribution of the sample mean of sample size n is obtained here as:

Therefore the probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0 is the reqd. probability here.

b) The probability that the sample mean lies between 275000 and 290000 is computed here as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0 is the required prob. here.