Question

dillon counted the pages in each book on his english classs required reading list. pages per book 44 44 44 162 779 779 779 779 779 779 x is the number of pages that a randomly chosen book had. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Calculate total number of books

There are 3 books with 44 pages, 1 book with 162 pages and 6 books with 779 pages. So the total number of books $n=3 + 1+6=10$.

Step2: Calculate the expected - value formula

The formula for the expected value $E(X)=\sum_{i}x_ip_i$, where $x_i$ is the value of the random - variable and $p_i$ is the probability of that value. Here, $p_1=\frac{3}{10}$ for $x_1 = 44$, $p_2=\frac{1}{10}$ for $x_2 = 162$ and $p_3=\frac{6}{10}$ for $x_3 = 779$.

Step3: Calculate the expected value

$E(X)=44\times\frac{3}{10}+162\times\frac{1}{10}+779\times\frac{6}{10}$
$=\frac{44\times3 + 162\times1+779\times6}{10}$
$=\frac{132 + 162+4674}{10}$
$=\frac{4968}{10}=496.8$

Answer:

$496.8$