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 (chart with x-axis 1,2,3,4,5 and y-axis probability) options: 0.2, 0.4, 1, 3

Explanation:

Step1: Identify Probabilities

From the graph, \( P(1) = 0.1 \), \( P(2) = 0.2 \), \( P(3) = 0.4 \), \( P(4) = 0.2 \), \( P(5) = 0.1 \).

Step2: Calculate Expected Value (Mean)

The formula for the mean \( \mu \) of a discrete probability distribution is \( \mu = \sum x \cdot P(x) \).
So, \( \mu = (1 \cdot 0.1) + (2 \cdot 0.2) + (3 \cdot 0.4) + (4 \cdot 0.2) + (5 \cdot 0.1) \).
Calculate each term:
\( 1 \cdot 0.1 = 0.1 \),
\( 2 \cdot 0.2 = 0.4 \),
\( 3 \cdot 0.4 = 1.2 \),
\( 4 \cdot 0.2 = 0.8 \),
\( 5 \cdot 0.1 = 0.5 \).

Sum these terms: \( 0.1 + 0.4 + 1.2 + 0.8 + 0.5 = 3 \).

Answer:

3