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# If bolt thread length is normally distributed, what is the ISBN: 9780321629111 32

## Solution for problem 44E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 44E

If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is a.? ithin 1.5 SDs of its mean value? b.? ?Farther than 2.5 SDs from its mean value? c.? ?Between 1 and 2 SDs from its mean value?

Step-by-Step Solution:

Solution: Step 1: It is given that the bolt thread length is normally distributed, we have to find the probability that the thread length of normally selected bolt is Within 1.5SDs of its mean value Farther than 2.5SDs from its mean value. Between 1 and 2 SDs from its mean value. Step 2 : a) We have to find the probability that the length of a randomly selected bolt is within 1.5SDs of its mean value. Let X be the thread length of the bolt. It is given that the bolt thread length follow normal distribution. So it will be P(-1.5 z 1.5) = P( Z 1.5) - P(Z-1.5) From the standard normal table we will get the probability F(-1.5) = 0.9332 F( 1.5) = 0.0668 That is P(-1.5 z 1.5) = F( 1.5) - F(-1.5) = 0.8664 b) We have to find the probability that the thread length of randomly selected bolt is farther than 2.5 SDs from its mean value. That is The required probability = P(Z> 2.5) P(Z> 2.5) = 1-P(Z2.5) From the standard normal table we will get P(Z2.5) = 0.9938 P(Z> 2.5) = 1-0.9938 = 0.0062

Step 3 of 3

##### ISBN: 9780321629111

The full step-by-step solution to problem: 44E from chapter: 4 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. Since the solution to 44E from 4 chapter was answered, more than 966 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. The answer to “If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is a.? ithin 1.5 SDs of its mean value? b.? ?Farther than 2.5 SDs from its mean value? c.? ?Between 1 and 2 SDs from its mean value?” is broken down into a number of easy to follow steps, and 48 words. This full solution covers the following key subjects: mean, sds, its, bolt, thread. This expansive textbook survival guide covers 18 chapters, and 1582 solutions.

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