Question

Alice passes through four tra¢ c lights on her way to work, and each light is equally likely to be green or red, independent of the others. Suppose that each red light delays Alice by exactly two minutes. What is the variance of Aliceís commuting time?

Answer 1

Using the binomial distribution, it is found that the variance of Alice's commuting time is of 2 minutes squared.

For each light, there are only two possible outcomes, either it is red, or it is green. The lights are independent of others, hence the binomial distribution is used to solve this question.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The variance of the binomial distribution is:

$V(X) = np(1 - p)$.

In this problem:

• She passes through four lights, hence n = 4.

• The lights are equally as likely to be red or green, hence p = 0.5.

The variance for the number of red lights is:

V(X) = 4(0.5)(0.5) = 1

Since each red light delays Alice by exactly two minutes, the variance of Alice's commuting time is of:

2 x 1 = 2 minutes squared.

More can be learned about the binomial distribution at brainly.com/question/14424710