A popular summer event is Skee-Ball. For $2, a customer purchases three balls and attempts to roll each ball into a central target. The customer wins their $2 back and wins an additional $1 if they hit the target once, an additional $3 if they hit the target twice and an additional $5 if they hit the target three times. If the customer does not hit the target at all, they lose their initial $2. Access the data set labeled ”Skee-Ball” which reports the outcomes of 2,500 games for a single day’s operation of a Skee-Ball booth. (a) Define a random variable C (Customer Score) equal to the number of times a customer hits the target in each set of three rolls. How many possible outcomes of C are there? Report your answer as an integer. (b) Report the net profit ($) that the Skee-Ball booth achieved for the day. Report your answer as an integer. Hint: Estimate the PDF of C based on the relative frequencies: P(C = c) = Frequency of C = c / 2,500 (c) Report P(C = 0). Round your answer to three decimal places. (d) Report P(C = 1). Round your answer to three decimal places. (e) Report P(C = 2). Round your answer to three decimal places. (f) Report P(C = 3). Round your answer to three decimal places.

A popular summer event is Skee-Ball. For $2, a customer purchases three balls and attempts to roll each ball into a central target. The customer wins their $2 back and wins an additional $1 if they hit the target once, an additional $3 if they hit the target twice and an additional $5 if they hit the target three times. If the customer does not hit the target at all, they lose their initial $2. Access the data set labeled ”Skee-Ball” which reports the outcomes of 2,500 games for a single day’s operation of a Skee-Ball booth.

(a) Define a random variable C (Customer Score) equal to the number of times a customer hits the target in each set of three rolls. How many possible outcomes of C are there? Report your answer as an integer.

(b) Report the net profit ($) that the Skee-Ball booth achieved for the day. Report your answer as an integer. Hint: Estimate the PDF of C based on the relative frequencies: P(C = c) = Frequency of C = c / 2,500

(c) Report P(C = 0). Round your answer to three decimal places.

(d) Report P(C = 1). Round your answer to three decimal places.

(e) Report P(C = 2). Round your answer to three decimal places.

(f) Report P(C = 3). Round your answer to three decimal places.