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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Wires manufactured for use in a computer system are

Chapter 4, Problem 71E

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QUESTION:

Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms. The actual measured resistances of the wires produced by company A have a normal probability distribution with mean .13 ohm and standard deviation .005 ohm.

a What is the probability that a randomly selected wire from company A’s production will meet the specifications?

b If four of these wires are used in each computer system and all are selected from company A, what is the probability that all four in a randomly selected system will meet the specifications?

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QUESTION:

Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms. The actual measured resistances of the wires produced by company A have a normal probability distribution with mean .13 ohm and standard deviation .005 ohm.

a What is the probability that a randomly selected wire from company A’s production will meet the specifications?

b If four of these wires are used in each computer system and all are selected from company A, what is the probability that all four in a randomly selected system will meet the specifications?

ANSWER:

Step 1 of 4

a.

Problem

To find the probability of wires produced with resistance between .12 and .14 ohms.

Given

The population of resistance of wires is normally distributed

Population mean, \(\mu=.13 \ \mathrm{ohm}\)

Population standard deviation, \(\sigma=.005 \ \mathrm{ohm}\).

Lower limit of random normal variable Y, Yl = 0.12 ohm.

Upper limit of random normal variable Y, Yu = 0.14 ohm.

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