5. A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow: Age less than 21 Age 21 or greater White 10 5 Black 20 50 Lime 25 15 Orange 35 25 Red 10 5 (1). What is the probability of randomly selecting a person who likes white cell phones the best? (2). What is the probability that black or orange are the favorite colors? (3). What is the probability that orange is the favorite color, given that the person's age is less than 21? (4). What is the probability that black is the favorite color, given that the person's age is 21 or older? (5). What is the probability that red is the favorite color, given that the person's age is 21 or older? (6). What is the probability that black, lime, or orange are the favorite colors, given that the person's age is 21 or older? 6. For the following probability distribution: X P(x) 10 .1 11 .25 12 .3 13 .25 14 .1 (1) The mean is (2) The variance is (3) The standard deviation is 7. A study conducted by a local tennis center revealed that 25 percent of its new members have novice level tennis skills. A membership drive in a metropolitan area resulted in 500 new members. It has been suggested that the normal approximation to the binomial be used to calculate various probabilities. (1) In this problem, can the normal approximation to the binomial be applied? (2) What is the mean and standard deviation to apply the normal approximation to the binomial? (3) What is the probability that 150 or more of the new members are novice tennis players? (4) What is the probability that 1 10 or less of the new members are novice tennis players? (5) What is the probability that between 1 10 and 130 of the new members are novice tennis players