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ISBN: 9781118539712 55

## Solution for problem 149E Chapter 3.8

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 149E

A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blade is found, the assembly is replaced with a newly sharpened set of blades.

(a) If 10 of the blades in an assembly are dull, what is the probability that the assembly is replaced the first day it is evaluated?

(b) If 10 of the blades in an assembly are dull, what is the probability that the assembly is not replaced until the third day of evaluation? [Hint: Assume that the daily decisions are independent, and use the geometric distribution.]

(c) Suppose that on the first day of evaluation, 2 of the blades are dull; on the second day of evaluation, 6 are dull; and on the third day of evaluation, 10 are dull. What is the probability that the assembly is not replaced until the third day of evaluation? [Hint: Assume that the daily decisions are independent. However, the probability of replacement changes every day.]

Step-by-Step Solution:

Step 1 of 4:

It is given that there are 48 blades in a slitter assembly. To check the sharpness of the blades, 5 blades are selected at random each day and the assembly is replaced with new set of blades if any dull blade is found.

Using this we need to find the required values.

Step 2 of 4:

(a)

It is given that in an assembly there are 10 dull blades.

We need to find the probability that this assembly is replaced on the first day it is evaluated.

Let X be the number of days.

Then X~Hypergeometric distribution(N=48,n=5,K=10).

P(X=x)=

=

Now we have to find the value of P(XIt is given by

P(X)=1-P(X<1)

=1-P(X=0)

=1-

=1-

=1-0.2931

=0.7069

Thus, the probability that the assembly with 10 dull blades is replaced on the first day is 0.7069.

Step 3 of 4

Step 4 of 4

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