Question

A population has a mean of 200 and a standard deviation of 90. Suppose a sample of size 125 is selected and is used to estimate . Use z-table.

a. What is the probability that the sample mean will be within +/- 9 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.) b. What is the probability that the sample mean will be within +/- 11 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Answer 1

Here we have

(a)

The z-score for is

The z-score for is

The probability that the sample mean will be within +/- 9 of the population mean is

(b)

The z-score for is

The z-score for is

The probability that the sample mean will be within +/- 11 of the population mean is