Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

The data that follow are the number of passengers on 35 different charter fishing boats. The sample mean = 7.9 and the sample standard deviation = 4.33. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. State the values of $a$ and $b$ . Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.

Distribution of proper notation $X ~ U (0, 14)$

The value of the theoretical mean is $7$ .

The value of standard deviation is $4.04$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

Given in the question that a table with the number of passengers on $35$ different charter fishing boats.

The sample mean $=$ $7.9$ and the sample standard deviation $= 4.33$ .

We need to determine the values of $a$ and $b$

We have to write the distribution in proper notation, and calculate the theoretical mean and standard deviation.

Step 2: Vales of a and b

Let's consider the above table

From the table , the lowest values is $0$ and the highest value is $14$ .

Therefore, the variable $a = 0$

$b = 14$

Hence, the provided data follows the uniform distribution such that $X ~ U (0, 14)$

Step 3: Calculate the theoretical mean

The theoretical mean of the uniform distribution is $μ = \frac{a + b}{2}$

Place the value of $a a n d b$

Therefore,

$μ = \frac{0 + 14}{2}$

$= \frac{14}{2}$

$= 7$

Step 4: Calculate the standard deviation

The standard deviation of the uniform distribution is $σ = \sqrt{\frac{(b - a)^{2}}{12}}$

Place the value of $a a n d b$

Now,

$σ = \sqrt{\frac{(14 - 0)^{2}}{12}}$

$= \sqrt{\frac{196}{12}}$

localid="1647957978309" $= \sqrt{16.33}$

$\approx 4.04$

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