Question

tucker counted the number of words per page in his new book. words per page 57 147 147 147 147 155 177 177 177 177 x is the number of words that a randomly - chosen page has. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Count the frequency of each value

The value 57 appears 1 time, 147 appears 4 times, 155 appears 1 time, 177 appears 4 times. The total number of data - points is $1 + 4+1 + 4=10$.

Step2: Use the expected - value formula

The expected - value formula for a discrete random variable $X$ is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible values of $X$ and $p_i$ are their corresponding probabilities.
The probability of a value $x_i$ is $p_i=\frac{n_i}{N}$, where $n_i$ is the frequency of $x_i$ and $N$ is the total number of data - points.
$E(X)=57\times\frac{1}{10}+147\times\frac{4}{10}+155\times\frac{1}{10}+177\times\frac{4}{10}$
$=\frac{57\times1 + 147\times4+155\times1 + 177\times4}{10}$
$=\frac{57+588 + 155+708}{10}$
$=\frac{1508}{10}=150.8$

Answer:

$150.8$