Question

find the mean (expected value) of the probability distribution.

Explanation:

Step1: Recall the formula for the mean of a probability distribution

The formula for the mean (expected value) \( E(X)\) of a discrete probability distribution is \( E(X)=\sum_{i}x_{i}P(x_{i})\), where \( x_{i}\) are the values of the random variable and \( P(x_{i})\) are their corresponding probabilities.

Step2: Calculate each term \( x_{i}P(x_{i})\)

• For \( x = 75\) and \( P(75)=0.12\): \(75\times0.12 = 9\)
• For \( x = 80\) and \( P(80)=0.23\): \(80\times0.23=18.4\)
• For \( x = 85\) and \( P(85)=0.42\): \(85\times0.42 = 35.7\)
• For \( x = 90\) and \( P(90)=0.11\): \(90\times0.11=9.9\)
• For \( x = 95\) and \( P(95)=0.12\): \(95\times0.12 = 11.4\)

Step3: Sum up the terms

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Answer:

\(84.4\)