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Q 52

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Introductory Statistics

Found in: Page 430

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

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

$11.05$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $μ = 10$ months and the sample size is 64.

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 $m$ is the decay parameter is given as:

$f (X) = m e^{(- m x)}$

Where, $X \geq 0 and m > 0$

The exponential distribution's standard deviation is $σ = μ = 10 .$

Step 3: Distribution Of Mean

If, $\bar{X}$ is the average length of time that 64 batteries last, the distribution of mean length for 64 batteries will be normal. The distribution of $\bar{X}$ is the mean length time of 64 batteries last is given as below:

$\bar{X} - N (μ_{X}, σ_{X} / \sqrt{n})$

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

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

Most popular questions for Math Textbooks

The mean number of minutes for app engagement by a tablet use in $8.2$ minutes. Suppose the standard deviation is one minute . Take a sample size of $70$ .

a. What is probability of that the sum of the sample is between seven hours and ten hours? What does this mean in context of the problem ?

b. Find the $84^{t h}$ and $16^{t h}$ percentiles for the sum of the sample. interprets these values in context.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

a) What is the distribution for the sum of the weights of 100 25-pound lifting weights?

b) Find P(Σx < 2,450).

7.7 The mean number of minutes for app engagement by a table use is $8.2$ minutes. Suppose the standard deviation is one minute. Take a sample size of $70$ .
a. What is the probability that the sum of the sample is between seven hours and ten hours? What does this mean in context of the problem?b. Find the $84^{th}$ and $16^{th}$ percentiles for the sum of the sample. Interpret these values in context.

What is $P (Σ x = 290)$ ?

In order for the sums of distribution to approach a normal distribution, what must be true?

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