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Q.4.8

Expert-verified
Found in: Page 253

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# 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 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

$\mu =SumofXP\left(X\right)$

Sum of values in the fourth column of the above table

$1.08-9.898\phantom{\rule{0ex}{0ex}}=-8.812$

$S\mathrm{tan}darddeviation=Sumrootof{\left(X-\mu \right)}^{2}P\left(X\right)\phantom{\rule{0ex}{0ex}}=\sqrt{127.872+1.3961}\phantom{\rule{0ex}{0ex}}=\sqrt{129.2686}\phantom{\rule{0ex}{0ex}}=11.36$

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.