dillon counted the pages in each book on his english classs required reading list. pages per book 44 44 44…

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.

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.

Answer

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:

$496.8$