Question

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

Explanation:

Step1: Recall mean formula for discrete - random variable

The mean $\mu$ of a discrete - random variable $X$ with probability distribution $P(X)$ is given by $\mu=\sum_{i}x_{i}P(x_{i})$, where $x_{i}$ are the values of the random variable and $P(x_{i})$ are their corresponding probabilities.

Step2: Multiply each value of $X$ by its probability

For $x_1 = 0.5$, $P(x_1)=0.07$, so $x_1P(x_1)=0.5\times0.07 = 0.035$.
For $x_2 = 1$, $P(x_2)=0.2$, so $x_2P(x_2)=1\times0.2 = 0.2$.
For $x_3 = 1.5$, $P(x_3)=0.46$, so $x_3P(x_3)=1.5\times0.46 = 0.69$.
For $x_4 = 2$, $P(x_4)=0.2$, so $x_4P(x_4)=2\times0.2 = 0.4$.
For $x_5 = 2.5$, $P(x_5)=0.07$, so $x_5P(x_5)=2.5\times0.07 = 0.175$.

Step3: Sum up the products

$\mu=0.035 + 0.2+0.69 + 0.4+0.175=1.5$.

Answer:

$1.5$