Statistics Canada reports that of people who usually work fu

Statistics Canada reports that of people who usually work full time, the average number of hours worked per week is 42.2. Assume that the number of hours worked per week for those who usually work full time is normally distributed. Suppose 12% of these workers work more than 45 hours. Based on this percentage, what is the standard deviation of number of hours worked per week for these workers?

Solution

For a right tailed area of 0.12, the corresponding z score is, by table/technology,

z = 1.174986792

Thus, as

sigma = (x - u)/z

Then

sigma = (45 - 42.2)/1.174986792

sigma = 2.38300551 [ANSWER]