The probability distribution graph of the random variable Y is a binomial distribution with a shape that is roughly symmetric, with the highest likelihood around the mean, which is 5.5, so the peak should be at Y = 5 or Y = 6.
To create a probability distribution graph for the random variable Y, which represents the number of times Pedro encounters a red light in 10 randomly selected work days, we use the binomial distribution where the probability of success (the light being red) is 55% or 0.55. Since we are selecting 10 days, our distribution will have the form Y ~ B(10, 0.55). The possible values for Y can range from 0 (no red lights on any day) to 10 (red light every day).
The shape of this binomial distribution will not be uniform, and it will likely be roughly symmetric around its mean. The mean of Y is given by the formula n*p, where 'n' is the number of trials and 'p' is the probability of success. Therefore, the mean is 10 * 0.55 = 5.5. Since we can't have half occurrences, we would expect the peak of the distribution to be at Y = 5 or Y = 6. Based on this, the closest answer is E), implying a roughly symmetric distribution with a peak at Y = 6.
The probable question may be:
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.