Question

Dr. Wu, a pediatrician, weighed all the children who recently visited his office. Weight (lbs) Number of children 10 2 41 6 49 4 61 4. 85 3 87 2 98 4 X is the weight that a randomly chosen child weighed. What is the expected value Write your answer as a decimal.

Answer 1

The expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].

The number of children = 2 + 6 + 4 + 4 + 3 + 2 + 4 = 25 children

The possibilities are their weights, so:

10 pounds

41 pounds

49 pounds

61 pounds

85 pounds

87 pounds

98 pounds

The probabilities of each possibilities are:

10 pounds - 2/25

41 pounds - 6/25

49 pounds - 4/25

61 pounds - 4/25

85 pounds - 3/25

87 pounds - 2/25

98 pounds - 4/25

Now, we find the expected value using the formula [E(x) is the expected value of x]:

`\begin{gathered} E(x)=(10)((2)/(25))+(41)((6)/(25))+(49)((4)/(25))+(61)((4)/(25))+(85)((3)/(25))+(87)((2)/(25))+(98)((4)/(25)) \\ =61.08 \end{gathered}`