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Chapter 7: Q 50 (page 430)

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

What is the distribution for the total length of time 64 batteries last?

Short Answer

Expert verified

The distribution for the total length of time 64 batteries last.10month.

Step by step solution

01

:Given Information

According to the given details,

The mean of the distribution is 渭=10months.

The sample size is64.

02

Explanation

From the information, we know that the probability density function of the exponential distribution

X~Exp(m)

where mis the decay parameter.

Therefore,

localid="1649332271197" f(X)=me(-mx)

localid="1649332290236" Where,X鈮�0andm>0.

Consider, X炉as the mean length time of 64batteries last, then the distribution of mean length of 64 batteries will follow the normal distribution.

The distribution of X炉is the mean length time of 64batteries last is given as follow:

X炉-N渭X,蟽X/n

X炉-N(10,10/64)

X炉~N(10,10/8)

Therefore, the distribution for total length of 64batteries last is:

m=1渭

=.10month

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