Question

QUESTION 1. The Bates Motel has 12 rooms available to rent this evening, but they have overbooked and made 14 room reservations. The probability a person cancels their room reservation is 0.11 independent of each other person. Let X represent the number of room reservations that are cancelled for this evening. (a) What is the probability distribution of X? State the name of the probability distribution and the value(s) of any relevant parameter(s). (b) How many room reservations would you expect to be cancelled? (c) Use the procedure demonstrated in Lab #2 to create a probability distribution table for X. (d) What is the probability that there will be a room available for every person who keeps their reservation? You may use the values obtained in part (c) as necessary, but you still need to explain your reasoning using probability statements/notation. (e) Show how to compute P(X = 4) = p(4) by hand. (f) Use the procedure demonstrated in Lab #2 to create a probability histogram for X. How would you describe the shape of the probability distribution? Could you have guessed this would be the shape using only the information in part (a)? Explain. QUESTION 2. An investment broker claims the annual return on an investment portfolio follows a normal distribution with a mean of 13 percent and a standard deviation of 21 percent. Let X represent the annual return on this investment portfolio for 2022. (a) What is the probability the investment portfolio yields a negative return? (b) What is the probability the investment portfolio yields a return of at least 5 percent? (c) What is the probability the investment portfolio yields a return between 0 percent and 5 percent? (d) Forty percent of the time the investment portfolio will yield a percentage return below what amount?

Answer 1