At a Large Business, Employees Must Report to Work at 7:30

At a large business, employees must report to work at 7:30 A.M. The arrival times of
employees can be described by a Normal model with mean of 7:22 A.M. and a standard
deviation of 4 minutes.
(SHOW WORK)
a. What percent of employees are late on a typical work day?
b. A psychological study determined that the typical worker needs five minutes to adjust to
their surroundings before beginning their duties. What percent of this business' employees
arrive early enough to make this adjustment?
c. Because late employees are a distraction and cost companies money, all employees need
to be on time to work. If the mean arrival time of employees does not change, what
standard deviation would the arrival times need to ensure virtually all employees are on
time to work?
d. Explain what achieving a smaller standard deviation means in the context of this
problem.