The mean number of hours that American women who worked outside of the home per week was 34.6 hours with a standard deviation of 13.6 hours. If 37 American women who worked outside of the home are randomly selected, what is the probability their mean hours worked per week is between 32 and 36 hours per week

0.61196

Step-by-step explanation:

When we are given a random number of samples , we solve using the z score formula

z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean = 34.6

σ is the population standard deviation = 13.6

n is the random number of samples = 37

For x = 32

z = 32 - 34.6/13.6/√37

z = -1.16288

Probability value from Z-Table:

P(x = 32) = 0.12244

For x = 36

z = 36 - 34.6/13.6/√37

z = 0.62617

Probability value from Z-Table:

P(x = 36) = 0.7344

The probability their mean hours worked per week is between 32 and 36 hours per week is calculated as:

P(x = 36) - P(x = 32)

= 0.7344 - 0.12244

= 0.61196