The manufacture of a certain part requires two different machine operations. The time on machine 1 has mean 0.5 hours and standard deviation 0.4 hours. The time on machine 2 has mean 0.6 hours and standard deviation 0.5 hours. The times needed on the machines are independent. Suppose that 100 parts are manufactured.

a. What is the probability that the total time used by machine 1 is greater than 55 hours?

b. What is the probability that the total time used by machine 2 is less than 55 hours?

c. What is the probability that the total time used by both machines together is greater than 115 hours?

d. What is the probability that the total time used by machine 1 is greater than the total time used by machine 2?

Solution

Step 1 of 7

Let X1 represents the time in machine 1

Let X2 represents the time in machine 2

Here the sample size 100

The total time on machine 1 has mean =0.5(100)=50

Standard deviation =0.4

=4

The total time on machine 2 has mean =0.6 (100)=60

Standard deviation =0.5

=5