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 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

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

The probability distribution of Y can be represented by a binomial distribution. The probability mass function of a binomial distribution is given by:

P(Y = y) = (n choose y) * p^y * (1 - p)^(n - y)

Where:

The number of trials = n

The probability of success = p

The number of successes = y

Here, n = 10 and p = 0.55.

A graph of the probability distribution of Y plots the probability mass function for each value of y from 0 to 10. The graph will have a bell-shaped curve, with the peak at y = 5.5 ≈ 6.

Thus, the shape of the probability distribution is approximately symmetric.