PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 10.4, Problem 53E
Solution
a.
To determine: the expected value of the game.
The expected value of the game is 4.5
Given information:
The square root of the expected value of squared deviations from the mean,
Concept Used:
The mean of a discrete probability distribution, where x is each value of random variables and
Calculation:
Calculate the mean using the formula for the mean of probability distribution.
b.
To determine: the standard deviation of the value of the prizes
The standard deviation of the value of the prizes is 13.96.
Given information:
The square root of the expected value of squared deviations from the mean,
Calculation:
The expected value of the game is 4.5.
Substitute all the values in
c.
To explain: why the standard deviation is so large.
The standard deviation is large since the data points are spread out over a large range of values.
Given information:
The square root of the expected value of squared deviations from the mean,
Calculation:
The expected value of the game is 4.5.
The standard deviation of the value of the prizes is 13.96. Notice that the standard deviation
d.
To explain: why are willing to pay $5 to play this game.
No, since the expected value is lower there is no high chance to win money in the long run.
Given information:
The square root of the expected value of squared deviations from the mean,
Calculation:
The expected value of the game is 4.5.
The standard deviation of the value of the prizes is 13.96. Whereas, the fee is $5 which is higher than the expected value.
Since the expected value is lower there is no high chance to win money in the long run.
Chapter 10 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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