Question

an employee at the craft store counted the number of red buttons in each bag of mixed buttons. red buttons per bag 50 73 73 94 94 94 94 102 102 102 x is the number of red buttons that a randomly - chosen bag had. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Calculate total number of bags

There are 10 data - points, so $n = 10$.

Step2: Calculate sum of all red - button counts

$50+73 + 73+94+94+94+94+102+102+102=50 + 2\times73+4\times94+3\times102=50+146 + 376+306=878$.

Step3: Calculate expected value

The expected value $E(X)=\frac{\text{Sum of all values}}{\text{Number of values}}$. So $E(X)=\frac{878}{10}=87.8$.

Answer:

$87.8$