Question

a machine dispensed red gumdrops into bags of various sizes. x is the number of red gumdrops 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 gumdrops

Multiply number of gumdrops by number of bags for each row and sum.
$$44\times2 + 51\times3+84\times3 + 177\times2$$
$$=88+153 + 252+354$$
$$=847$$

Step2: Calculate total number of bags

Sum the number of bags.
$$2 + 3+3 + 2=10$$

Step3: Calculate expected value

Expected value \(E(X)=\frac{\text{Total gumdrops}}{\text{Total bags}}\)
$$E(X)=\frac{847}{10}=84.7$$

Answer:

\(84.7\)