Identify if the following scenarios describe a discrete or continuous random variable.

Explain your choice.

(a) X = The number of persons in an emergency room

(b) W = The weights of delivery trucks at a supermarket.

(c) H = The areas of houses being built in a new subdivision.

18. Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let X =

the number of free throws Faith makes out of 20 shots.

(a) Explain why X is a binomial random variable.

(b) Calculate and interpret the mean of X.

(c) Calculate and interpret the standard deviation of X.

(d) Use the binomial probability formula to find P(X = 19). Interpret this value in context.

(e) Her coach says that he will let the team out of practice early if Faith makes 18 or more free

throws. What is the probability that practice ends early? Show your work.

19. Let Y = the number of siblings for a student at a local high school. Suppose we choose

someone from the school at random. The probability distribution of Y is as follows.

(a) Is Y a discrete or continuous? Explain.

(b) Is this a valid probability distribution? Explain.

(c) Create a histogram for the probability distribution and describe its shape.

(d) Find the probability that the randomly selected student has at least one sibling.

(e) Describe in words what P(Y>2) means and find the probability.