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Q.4.8

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Introductory Statistics

Found in: Page 253

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

On May 11, 2013 at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next $48$ hours in Japan was about $1.08 %$ . As in Example $4.8$ , you bet that a moderate earthquake will occur in Japan during this period. If you win the bet, you win $$ 100$ . If you lose the bet, you pay $$ 10$ . Let X = the amount of profit from a bet. Find the mean and standard deviation of X.

Mean= Expected value $= - 8.812$

Standard deviation $= 11.3696$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Content Introduction

To find mean and deviation of X, let us first make the following table with the given information:

Step 2: Content Explanation

Mean = Expected value

$μ = S u m o f X P (X)$

Sum of values in the fourth column of the above table

$1.08 - 9.898 = - 8.812$

$S \tan d a r d d e v i a t i o n = S u m r o o t o f {(X - μ)}^{2} P (X) = \sqrt{127.872 + 1.3961} = \sqrt{129.2686} = 11.36$

Therefore, there is an average loss of amount $$ 8.81$ per bet with a standard deviation of amount $$ 11.36$ in the average loss per bet in the long run.

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