a veterinarian weighed all the dogs that visited her office last month. dogs weights (lbs) 71 71 71 88 160…

a veterinarian weighed all the dogs that visited her office last month. dogs weights (lbs) 71 71 71 88 160 160 160 174 174 174. x is the weight that a randomly chosen dog weighed. what is the expected value of x? write your answer as a decimal.

a veterinarian weighed all the dogs that visited her office last month. dogs weights (lbs) 71 71 71 88 160 160 160 174 174 174. x is the weight that a randomly chosen dog weighed. what is the expected value of x? write your answer as a decimal.

Answer

Explanation:

Step1: Count the frequencies

There are 3 dogs weighing 71 lbs, 1 dog weighing 88 lbs, 3 dogs weighing 160 lbs, and 3 dogs weighing 174 lbs. The total number of dogs $n=3 + 1+3 + 3=10$.

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 and $p_i$ is the probability. The probability $p_i=\frac{\text{frequency of }x_i}{n}$. $E(X)=71\times\frac{3}{10}+88\times\frac{1}{10}+160\times\frac{3}{10}+174\times\frac{3}{10}$

Step3: Perform the multiplications

$71\times\frac{3}{10}=21.3$, $88\times\frac{1}{10}=8.8$, $160\times\frac{3}{10}=48$, $174\times\frac{3}{10}=52.2$

Step4: Sum up the results

$E(X)=21.3 + 8.8+48+52.2=130.3$

Answer:

$130.3$