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.

a. What is the standard deviation?

b. What is the parameter m ?

Short answer

1. The standard deviation is 10
2. The parameter m is 0.1

Step-by-step solution

Part (a)Step 1 Given Information of 

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.

Part (a) 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:

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

Where and $m>0$. The standard deviation of the exponential distribution is given as below:

$\sigma =\mu$

=10

Part (b) 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.

Part (b) Step 2: Explanation 

The exponential distribution$X~Exp\left(m\right)$, where$m$is the decay parameter, which is given as below:

$m=\frac{1}{\mu }$

$=\frac{1}{10}$

=0.1