Question

Ms. Hensley reported her students' scores on the most recent quiz. Score Number of students 5 6 40 2 41 3. 46 4 55 1 89 2 97 2 X is the score that a randomly chosen student scored. What is the expected value of X? Write your answer as a decimal.

Answer 1

Let the total number of students be s.

Then,

s = 6 + 2 + 3 + 4 + 1 + 2 + 2 = 20

Score(x) | Number of students(n) | Pr(x) = n / s | xPr(x)

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5 | 6 | 0.30 | 1.5

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40 | 2 | 0.10 | 4.0

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41 | 3 | 0.15 | 6.15

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46 | 4 | 0.20 | 9.20

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55 | 1 | 0.05 | 2.75

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89 | 2 | 0.1 | 8.90

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97 | 2 | 0.1 | 9.7

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`\begin{gathered} \text{ The expected value is } \\ \sum x(Pr(x))=1.50+4.00+6.15+9.20+2.75+8.90+9.70=42.2 \end{gathered}`

Hence,

the expected value is 42.2