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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

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

Step by step solution

01

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 μ=10months and the sample size is 64.

02

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(m), where mis the decay parameter is given as:

f(X)=me(-mX)

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

σ=μ

=10

03

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 isμ=10months and the sample size is 64.

04

Part (b) Step 2: Explanation 

The exponential distributionX~Exp(m), wheremis the decay parameter, which is given as below:

m=1μ

=110

=0.1

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