Question

The U.S. Census Bureau announced that the population mean sales of houses was $322,100. Assume that the standard deviation of the prices is $90,000. If you select a sample size of 100, what’s the cumulative probability that the sample mean will be less than $346,000 for all possible house samples?

Answer 1

P(z < 2.66) = 0.9960

Step-by-step explanation:

Given that

population mean = 322,100

standard deviation = 90,000

sample mean = 346,000

n = 100

Standard error of mean:

`=(Standard\ Deviation)/(√(n) )`

`=(90,000)/(√(100) )`

= 9000

`Z=(Sample\ mean-Population\ mean)/(Standard\ error\ of\ mean)`

`Z=(346,000-322,100)/(9,000)`

z = 2.66

P(z < 2.66) = 0.9960

Above value is computed from the z-tables.