Question

Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red on a randomly selected work day. Suppose we choose 10 of D

Pedro's work days at random and let Y = the number of times that the light is red.
Make a graph of the probability distribution of Y. What is the shape of the probability distribution?

A) The shape of the probability distribution is right-skewed with a single peak at Y = 10.

B) The shape of the probability distribution is uniform.

C) The shape of the probability distribution is roughly symmetric with a single peak at Y = 5.

D) The shape of the probability distribution is left-skewed with a single peak at Y = 8.

E) The shape of the probability distribution is roughly symmetric with a single peak at Y = 6.

Answer 1

C) The shape of the probability distribution is roughly symmetric with a single peak at Y = 5.

Explanation:

To create the probability distribution for the number of times the light is red (Y), you can use the binomial distribution formula. Given the probability of success (light is red) on a single trial (55%) and the number of trials (10 workdays), you can calculate the probabilities for each possible value of Y.

The correct answer is:

C) The shape of the probability distribution is roughly symmetric with a single peak at Y = 5.

The binomial distribution tends to be roughly symmetric when the probability of success is close to 0.5, and in this case, the probability of the light being red is 55%. The peak of the distribution occurs around the expected value, which is given by n * p (10 * 0.55 = 5.5, rounded to 5 in this case).