Question

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes.

i. What is the probability that a randomly selected individual will have a waiting time of at least 10 minutes?

ii. What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes?

iii. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?

b. Suppose that the distribution for a random variable � is normal with mean 15 and standard deviation (population), and p (x < 0) = 0.0773. Rounded to two decimal places, what is standard deviation for population?

c The monthly earnings of computer systems analysts are normally distributed with a mean of $4,300. If the probability that a systems analyst earns a monthly income of more than $6,140 is 0.015, what is the value of the standard deviation of the monthly earnings of the computer systems analysts?

Answer 1