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:

Identify the given values and formula

Using the Probability Distribution and Expected Value knowledge points

$$
LATEXBLOCK0
$$

Calculate the products of each value and its probability

Using the Expected Value knowledge point

$$
LATEXBLOCK1
$$

Sum the products to find the mean

Using the Expected Value knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) 0.20
• (B) 0.46
• (C) 0.85
• (D) 1.50 (Correct answer)