Concept explainers
To find: The expected value of the gift card won from the given options.
Answer to Problem 10PT
The expected value is $143.25. The correct option is C
Explanation of Solution
Given:
Thegiven table for the amount and the winners is shown in Table 1
Table 1
Amount, X | Winners |
$100 | 495 |
$125 | 405 |
$150 | 285 |
$200 | 180 |
$250 | 90 |
$300 | 45 |
Calculation:
Consider total number of gift cards won in a mall contest is,
The probability that the corresponding to each value of X by the use of the relation given as,
The table for the probability is shown in Table 2
Table 2
Amount, X | Winners | |
$100 | 495 | 0.33 |
$125 | 405 | 0.27 |
$150 | 285 | 0.19 |
$200 | 180 | 0.12 |
$250 | 90 | 0.06 |
$300 | 45 | 0.03 |
The expected value of the random variable is obtained as,
The expected value with the help of table is shown in Table 3
Table 3
Amount, X | Winners | ||
$100 | 495 | 0.33 | 33.00 |
$125 | 405 | 0.27 | 33.75 |
$150 | 285 | 0.19 | 28.50 |
$200 | 180 | 0.12 | 24 |
$250 | 90 | 0.06 | 15 |
$300 | 45 | 0.03 | 9 |
From above the sum of the expected value is $143.25.
Chapter 11 Solutions
Glencoe Algebra 2 Student Edition C2014
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