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The battery life of a certain fire alarm, denoted by X, follows an exponential distribution with...

The battery life of a certain fire alarm, denoted by X, follows an exponential distribution with mean 3 hours. Suppose we take a random sample of 36 fire alarms. Answer the following questions.

A. Find the probability that a single fire alarm will operate for at least 6 hours.

B. Find the probability that the total battery lifetime based on the 36 fire alarms will be more than 126 hours.

C.

If the sample mean was 3.5, find a 95% confidence interval for the mean of the battery life.

=> 95% confidence interval for the mean of the battery life:

D. How large a sample is needed if we wish to be 95% confident that our sample mean will be within 0.5 hours of the true mean?

Math   Statistics-And-Probability   
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