# In a process that manufactures bearings, 90% of the

## Problem 11E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Problem 11E

In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings.

a. What is the probability that a given shipment is acceptable?

b. What is the probability that more than 285 out of 300 shipments are acceptable?

c. What proportion of bearing must meet the specification in order than 99% of the shipments are acceptable?

Step-by-Step Solution:

Step 1 of 4</p>

Here  given 90% of the bearings meat a thickness specification

The p=0.9

A shipment contains 500 bearings

Let X represents no. of acceptable bearings

Then XB(500,0.9)

Here X is  approximately following the normal distribution

Mean(=np

=500(0.9)

=450

Variance =npq

=500(0.9)(0.1)

=45

Hence =

=6.71

Step 2 of 4</p>

a) Here we have to find the probability of the given shipment is acceptable

So we have to find P(X440)

Use the continuity correction find the Z value for 439.5

Then  Z=(

=(439.5-450)/6.71

= -1.56

Now find P(Z1.49) value from the standard normal tables

P(Z-1.56)=1-P(Z1.56)

=1-0.0606

=0.9394

Hence the probability of the given shipment is acceptable is 0.0681

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

The full step-by-step solution to problem: 11E from chapter: 4.11 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings.a. What is the probability that a given shipment is acceptable?________________b. What is the probability that more than 285 out of 300 shipments are acceptable?________________c. What proportion of bearing must meet the specification in order than 99% of the shipments are acceptable?” is broken down into a number of easy to follow steps, and 85 words. Since the solution to 11E from 4.11 chapter was answered, more than 1211 students have viewed the full step-by-step answer. This full solution covers the following key subjects: bearings, shipment, acceptable, specification, meet. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th.

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