Question

the results and develops the probability distribution below for a randomly selected student. what is the mean of the probability distribution?
probability distribution
hours
studied: x
probability: p(x)
0.5
0.07
1
0.2
1.5
0.46
2
0.2
2.5
0.07
0.20
0.46
0.85
1.50

Explanation:

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

The formula for the mean \(\mu\) of a discrete probability distribution is \(\mu=\sum_{i}(x_i\times P(x_i))\)

Step2: Calculate each product \(x_i\times P(x_i)\)

• For \(x = 0.5\) and \(P(x)=0.07\): \(0.5\times0.07 = 0.035\)
• For \(x = 1\) and \(P(x)=0.2\): \(1\times0.2=0.2\)
• For \(x = 1.5\) and \(P(x)=0.46\): \(1.5\times0.46 = 0.69\)
• For \(x = 2\) and \(P(x)=0.2\): \(2\times0.2 = 0.4\)
• For \(x = 2.5\) and \(P(x)=0.07\): \(2.5\times0.07=0.175\)

Step3: Sum up the products

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Answer:

\(1.50\)