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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.

Find the IQR for the mean amount of time 64 batteries last.

Short Answer

Expert verified

The IQR for the mean amount of time 64 batteries last is1.69 months

Step by step solution

01

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 μ=10 months and the sample size is 64.

02

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, X0andm>0

The exponential distribution's standard deviation isσ=μ=10

03

Step 3:  Distribution of Mean

If ,X¯is the average length of time that 64 batteries endure, then the distribution of the average length of 64 batteries will be normal. The following shows the distribution ofX¯which is the average length of time that 64 batteries last:

X¯-NμX,σX/n

X¯~N(10,10/64)

X¯~N(10,10/8)

04

Calculation

To calculate the Interquartile range, calculate 75thand the25thpercentile, use the T1-83 calculator. For this, click on 2nd, then DISTR, and then scroll down to the invNorm option and enter the provided details. After this, click on ENTER button of the calculator to get the result. The screenshot is given as below:

Therefore, the interquartile range (|QR) for the total length of time of 64 batteries last Is given as:

(IQR)=Q1-Q1

=10.8431-9.1568

=1.6862

=1.69 Months

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Most popular questions from this chapter

Based on data from the National Health Survey, women between the ages of 18and 24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18to 24follow a normal distribution.

a. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 120.

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c. If the sample were four women between the ages of18to 24 and we did not know the original distribution, could the central limit theorem be used?

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