According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 27 minutes.
a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be? 95%? 99.7%?
b. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 359 and 479 minutes?
c. Suppose a worker spent 400 minutes on the job. What would that worker’s z score be, and what would it tell the researcher?