Question

a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean of the probability distribution below?
probability distribution
0.2
0.4
1
3

Explanation:

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

The mean \(\mu\) of a discrete probability distribution is given by \(\mu=\sum_{i}x_ip(x_i)\), where \(x_i\) are the values of the random variable and \(p(x_i)\) are their corresponding probabilities.

Step2: Identify the values of \(x\) and \(p(x)\) from the graph

From the graph:

• When \(x = 1\), \(p(1)=0.1\)
• When \(x = 2\), \(p(2)=0.2\)
• When \(x = 3\), \(p(3)=0.4\)
• When \(x = 4\), \(p(4)=0.2\)
• When \(x = 5\), \(p(5)=0.1\)

Step3: Calculate the mean

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Answer:

3