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Expert-verified Found in: Page 430 ### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208 # 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. Find the 80th percentile for the total length of time 64 batteries last .

The 80th percentile for the total length of time 64 batteries last is approximately

$11.05$

See the step by step solution

## Step 1: Given Information

According to the given details, the length of time a particular smartphone's battery lasts follows the exponential distribution. The mean of the distribution is $\mu =10$ months and the sample size is 64.

## Step 2: Explanation

The exponential distribution is used to determine how long a smartphone's battery lasts. The exponential distribution's probability density function $X~Exp\left(m\right)$, where $m$is the decay parameter is given as:

$f\left(X\right)=m{e}^{\left(-mx\right)}$

Where, $X\ge 0\text{and}m>0$

The exponential distribution's standard deviation is $\sigma =\mu =10.$

## Step 3: Distribution Of Mean

If, $\overline{X}$ is the average length of time that 64 batteries last, the distribution of mean length for 64 batteries will be normal. The distribution of $\overline{X}$ is the mean length time of 64 batteries last is given as below:

$\overline{X}-N\left({\mu }_{X},{\sigma }_{X}/\sqrt{n}\right)$

$\overline{X}~N\left(10,10/\sqrt{64}\right)$

$\overline{X}~N\left(10,10/8\right)$ ### Want to see more solutions like these? 