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# The manufacture of a certain part requires two different ISBN: 9780073401331 38

## Solution for problem 18E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Problem 18E

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?

Step-by-Step Solution:

Step 1 of 7</p>

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

Step 2 of 7</p>

a) Here we have to find the probability that the total time used by machine 1 is greater than 55 hours

So we have to find P(X1>55)

For continuity correction find z for 55.5

For 55.5,   Z=( =(55.5-50)/4

=1.38

Now we have to find P(Z>1.38)=1-P(Z 1.38)

=1-0.91621

=0.08379

Hence the probability that the total time used by machine 1 is greater than 55 hours is 0.08379

Step 3 of 7</p>

b) Here we have to find the probability that the total time used by machine 2 is less than 55 hours

So we have to find P(X2< 55)

For continuity correction find z for 54.5

For 54.5,   Z=( =(54.5-50)/5

=0.9

Now we have to find P(Z 0.9)=0.81594

Hence the probability that the total time used by machine 2 is less than 55 hours is 0.81594

Step 4 of 7</p>

c) Here we have to find the probability of that the total time used by both machines together is greater than 115 hours

Let X=X1 +X2 represents the total time in two machines

Mean = =50+60

=110

Standard deviation = = =6.4

Step 5 of 7

Step 6 of 7

##### ISBN: 9780073401331

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