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Q 52

Expert-verifiedFound in: Page 430

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

$11.05$

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.

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:

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

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

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

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:

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

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

$\overline{X}~N(10,10/8)$

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