Problem 7

The amount of time spent by workers of a company to perform a certain task is normally distributed random variable with a mean of 7.5 hours and a standard deviation of 2.1 hours.

(a) (2.5 marks) What is the probability that a worker needs more than 10 hours to perform the task?

(b) (3 marks) Find the probability that a worker needs between 7 and 9 hours to perform the task.

(c) (2.5 marks) What is the probability that a worker needs less than 3 hours to perform the task?

(d) (4 marks) What is the amount of time below which 5% of all the workers perform the task?