A battery manufacturer claims that the lifetime of a

Chapter 4, Problem 16E

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QUESTION:

A battery manufacturer claims that the lifetime of a certain type of battery has a population mean of 40 hours and a standard deviation of 5 hours. Let \(\overline X\) represent the mean lifetime of the batteries in a simple random sample of size 100 .

a. If the claim is true, what is \(P(\overline X\leq36.7)\)?

b. Based on the answer to part (a), if the claim is true, is a sample mean lifetime of  hours unusually short?

c. If the sample mean lifetime of the 100 batteries were  hours, would you find the manufacturer's claim to be plausible? Explain.

d. If the claim is true, what is \(P(\overline X\leq39.8)\)?

e. Based on the answer to part , if the claim is true, is a sample mean lifetime of  hours unusually short?

f. If the sample mean lifetime of the 100 batteries were  hours, would you find the manufacturer's claim to be plausible? Explain.

Equation Transcription:

Text Transcription:

overline{X}

P(overline{X}{</=}36.7)

P(overline{X}{</=}39.8)

Questions & Answers

QUESTION:

A battery manufacturer claims that the lifetime of a certain type of battery has a population mean of 40 hours and a standard deviation of 5 hours. Let \(\overline X\) represent the mean lifetime of the batteries in a simple random sample of size 100 .

a. If the claim is true, what is \(P(\overline X\leq36.7)\)?

b. Based on the answer to part (a), if the claim is true, is a sample mean lifetime of  hours unusually short?

c. If the sample mean lifetime of the 100 batteries were  hours, would you find the manufacturer's claim to be plausible? Explain.

d. If the claim is true, what is \(P(\overline X\leq39.8)\)?

e. Based on the answer to part , if the claim is true, is a sample mean lifetime of  hours unusually short?

f. If the sample mean lifetime of the 100 batteries were  hours, would you find the manufacturer's claim to be plausible? Explain.

Equation Transcription:

Text Transcription:

overline{X}

P(overline{X}{</=}36.7)

P(overline{X}{</=}39.8)

ANSWER:

Solution

Step 1 of 7

Here given that the battery manufacturer claims that the lifetime of a certain type of a battery with population mean of 40 hrs and standard deviation of 5 hrs

So =40

      =5

Let represents the mean life of the sample

Here follows the normal distribution


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