Question

a teacher asks her students to write down the number of hours studied, rounded to the nearest half hour. she compiles 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

Explanation:

Step1: Recall mean formula

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

Step2: Calculate product for each pair

For $x_1 = 0.5$ and $P(x_1)=0.07$, the product is $0.5\times0.07 = 0.035$.
For $x_2 = 1$ and $P(x_2)=0.2$, the product is $1\times0.2=0.2$.
For $x_3 = 1.5$ and $P(x_3)=0.46$, the product is $1.5\times0.46 = 0.69$.
For $x_4 = 2$ and $P(x_4)=0.2$, the product is $2\times0.2 = 0.4$.
For $x_5 = 2.5$ and $P(x_5)=0.07$, the product is $2.5\times0.07=0.175$.

Step3: Sum up the products

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

Answer:

None of the provided options are correct. The mean of the probability distribution is $1.5$.