Question

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?

Answer 1

To find the standard deviation of the weekly work hours when 12% work more than 45 hours, we use the z-score corresponding to the 12% tail, which is 1.17, and solve for standard deviation using the formula: standard deviation = (x - mean) / z.

Step-by-step explanation:

To find the standard deviation of the number of hours worked per week by full-time workers, when provided with the mean and the percentage of workers who work more than a certain number of hours, we can use the properties of the normal distribution.

In this case, Statistics Canada reports an average of 42.2 hours with 12% working more than 45 hours a week. Since this is a right-tailed situation (we are looking above a certain value), the z-score corresponding to the 12% tail can be found using a z-table or normal distribution calculator, which is approximately 1.17.

The z-score formula z = (x - mean) / standard deviation can be rearranged to find the standard deviation: standard deviation = (x - mean) / z. Plugging in the values, we have: standard deviation = (45 - 42.2) / 1.17. Calculating this gives us the standard deviation of the number of hours worked per week for these workers.