The annual income of a large group of supervisors at Belco Industries follows the normal distribution. The mean amount earned yearly is $48,000 and the standard deviation is $1,200. The length of service of the same supervisors also follows the normal distribution, with a mean of 20 years and a standard deviation of 5 years. John McMaster earns $50,400 annually and has 10 years of service.
a. Compare his income with those of the other supervisors.
b. Compare his length of service with those of the other supervisors.
c. The president of Belco wants to give a bonus to those supervisors at the lower end of the income distribution. If he gives a bonus to the lowest 8 percent, what is the cutoff point between those who receive the bonus and those who do not?
The solution gives the details of normal probability calculation.