1. You are driving home from work, and get stuck in a traffic jam. You are consi

Question

1. You are driving home from work, and get stuck in a traffic jam. You are considering turning off from your usual route home and taking a longer route that might have less traffic. However, you know that there is some chance that the traffic on your usual, shorter route will clear up. Based on the table below, calculate the expected value (in minutes until you arrive home) of each option.

Instructions: Round your answers to the nearest whole number.

Route 1: Expected value = ___ minutes.

Route 2: Expected value = ___ minutes.

2. Books for Kids is a not-for-profit organization that runs after-school reading programs in four school districts. Books for Kids is planning a fundraiser to buy new books. Last time it held a fundraiser, donors were allowed to specify which district program they wanted to receive their donation. The table below shows the average donations and the percent of all donations that went to each district. Using the last fundraiser as a projection, what is the expected value of the average donation across all four programs?

Instructions: Round your answer to two decimal places.

The expected value of the average donation across all four districts is $____

Light traffic Moderate traffic Heavy traffic   Probability of encountering on Route 1 50% 20% 30%   Duration of drive on Route 1 20 minutes 30 minutes 40 minutes   Probability of encountering on Route 2 50% 50% 0%   Duration of drive on Route 2 30 minutes 70 minutes 60 minutes

Explanation / Answer

(1)

expected value, route 1 (minutes) = 50% x 20 + 20% x 30 + 30% x 40 = 10 + 6 + 12 = 28

expected value, route 2 (minutes) = 50% x 30 + 50% x 70 + 0% x 60 = 15 + 35 + 0 = 50

(2)

Expected value ($) = 10% x 25 + 30% x 50 + 20% x 15 + 40% x 14 = 2.5 + 15 + 3 + 5.6 = 26.10

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