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16. You found a shortcut to school that saves 5 minutes off of taking the freeway. About 1 in every 10 trips
you get stuck behind a bus and it ends up taking you 20 minutes longer than the freeway. What is the expected
value of the shortcut?

Sagot :

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Answer:

  it saves 2.5 minutes

Step-by-step explanation:

The expected value of a random variable is the sum of products of possibilities and the probability of each.

Here, you have a probability of 0.9 of saving 5 minutes, and a probability of 0.1 of adding 20 minutes.

__

The expected value of the shortcut is ...

  0.9(-5) +0.1(20) = -4.5 +2.0 = -2.5

The shortcut is expected to save 2.5 minutes on average.

_____

Additional comment

The probability of 0.9 comes from the 9 of 10 trips that result in a time saving.

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