Four people working independently on an assembly line all perform the same task. The time (in minutes) to complete this task for person i (i 5 1, 2, 3, 4) has a uniform distribution on the interval...

Four people working independently on an assembly line all perform the same task. The time (in minutes) to complete this task for person i (i 5 1, 2, 3, 4) has a uniform distribution on the interval [0, i]. Suppose each person begins the task at the same time.

a. What is the probability that person 2 takes less than 90 seconds to complete the task?

 b. What is the mean completion time for each person?

c. What is the probability that all four people complete the task in less than 30 seconds?

d. What is the probability that exactly one person completes the task in less than one minute?

The probability density function for a random variable X is given by