Question

A business magazine surveyed its readers about their commute times. Time (minutes) Number of commutes 0 2 3 3 13 1 15 3 37 1 X is the time of a randomly chosen commute. What is the expected value of X? Write your answer as a decimal.

Answer 1

The basic expected value formula is the probability of an event multiplied by the number of times the event happens: (P(x) * n).

Probability is given by = number of event/ number of total outcome

To obtain the expected value of X

We will have to get the probability for each of the Time

Total outcome = sum of the number of commutes

=> 2 + 3 + 1 + 3 + 1 = 10

pr(0)= 2/ 10 = 0.2

pr(3) = 3/10 = 0.3

pr(13) = 1/10 = 0.1

pr(15)= 3/10 = 0.3

pr(37)= 1/10 = 0.1

The expected value = 0 x 0.2 + 3 0.3 + 13 x 0.1 + 15 x 0.3 + 37 x 0.1

=> 0 + 0.9 + 1.3 + 4.5 + 3.7

=> 10.4

Expected value of X = 10.4