Question

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 mean length of time 64 batteries last?

Short answer

The distribution for the mean length of time 64 batteries last is $\overline{X}~N(10,10/8)$

Step-by-step solution

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.

Explanation

The length of time a particular smartphone's battery lasts follows the exponential distribution. The probability density function of the exponential distribution $X~Exp\left(m\right)$, where$m$is the decay parameter is given as:

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

$\text{Where,}X\ge 0\text{and}m>0\text{. The standard deviation of the exponential distribution is}\sigma =\mu =10\text{.}$