A technical assistance manager monitored his customers' wait times. Time (minutes) Number of people 4 4 24 4. 106 2 X is the time that a randomly chosen person waited for. What is the expected value of X? Write your answer as a decimal.

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JordanyG707145 JordanyG707145 · Answer 1 · 2022-10-28T01:20:46+02:00

Let p be the total number of people.

Therefore,

[tex]p=4+4+2=10[/tex]

Let the number of people that waited for a particular time,x, be n.

Therefore, the probability, Pr(x), that a person waited for a time x is given by

[tex]Pr(x)=\frac{n}{p}=\frac{n}{10}[/tex]

Now, we make a table as shown below

x | Number of people(n) | Pr(x) | xPr(x)

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4 | 4 | 0.4 | 1.6

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24 | 4 | 0.4 | 9.6

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106 | 2 | 0.2 | 21.2

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[tex]\text{ The expected value is }\sum \text{xPr(x)}[/tex]

[tex]\sum \text{xPr(x) = 32.4}[/tex]

Therefore, the expected value is 32.4 minutes