The diameter of an electric cable is normally distributed with average 0.8 and variance 0.0004. A cable is considered defective if the diameter differs from its average by more than 0.025a. What is the probability of obtaining a defective cable?b. If 10,000 cables are tested, what is the expected number of defective cables?c. If 4 of these cables are tested, what is the probability that there is at least one defective cable?

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Asked Nov 24, 2019
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The diameter of an electric cable is normally distributed with average 0.8 and variance 0.0004. A cable is considered defective if the diameter differs from its average by more than 0.025
a. What is the probability of obtaining a defective cable?
b. If 10,000 cables are tested, what is the expected number of defective cables?
c. If 4 of these cables are tested, what is the probability that there is at least one defective cable?

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Expert Answer

Step 1

a.

A cable is considered defective if the diameter differs from its average by more than 0.025 What is the probability of obtaining a defective cable

From the given information, the average is 0.8 and standard deviation is = 0.02 (sqrt 0.0004).

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Step 2

b.

if 10,000 cables are tested, the expected number...

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Expectednumber = testedcables xprobability of defective cables =np 10,000 (0.2113) =2,113

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