In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 5 days at random in January to go surfing. Let r be the number of days the surf is at least 6 feet. (a) What is the probability of getting 4 or more days when the surf is at least 6 feet? (Round your answer to three decimal places.)
(b) What is the probability of getting fewer than 2 days when the surf is at least 6 feet? (Round your answer to three decimal places.)
(c) What is the expected number of days when the surf will be at least 6 feet? (Round your answer to two decimal places.)
days
(d) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
days
(e) Can you be fairly confident that the surf will be at least 6 feet high on one of your days off? Explain. (Round your answer to three decimal places.)
Yes, because the probability of at least 1 day with surf of at least 6 feet is and the expected number of days when the surf will be at least 6 feet is greater than one.