Question

dr. cline, a pediatrician, weighed all the children who recently visited her office. childrens weights (lbs) 18 18 18 25 25 25 25 25 25 48 48 48 48 48 51 51 51 52 52 x is the weight that a randomly chosen child weighed. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Count the frequency of each weight

There are 3 children with weight 18 lbs, 7 children with weight 25 lbs, 5 children with weight 48 lbs, 3 children with weight 51 lbs, and 2 children with weight 52 lbs. The total number of children $n=3 + 7+5+3+2=20$.

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. The probability $p_i=\frac{f_i}{n}$, where $f_i$ is the frequency of the value $x_i$.
$E(X)=18\times\frac{3}{20}+25\times\frac{7}{20}+48\times\frac{5}{20}+51\times\frac{3}{20}+52\times\frac{2}{20}$

Step3: Calculate each term

$18\times\frac{3}{20}=\frac{54}{20}=2.7$
$25\times\frac{7}{20}=\frac{175}{20}=8.75$
$48\times\frac{5}{20}=12$
$51\times\frac{3}{20}=\frac{153}{20}=7.65$
$52\times\frac{2}{20}=\frac{104}{20}=5.2$

Step4: Sum up the terms

$E(X)=2.7 + 8.75+12+7.65+5.2$
$E(X)=36.3$

Answer:

$36.3$