The lifespan of a domesticated cat, Felis catus, is normally distribut deviation of 1 year. a. i. Find the probably that a randomly selected cat has a lifespan of more than 17.5 years. Give your answer correct to four decimal places. ii. Given that a particular cat is at least 14 years old, what is the probability that it will live longer than 17.5 years? Give your answer correct to four decimal places. The masses of the same species of cat are normally distributed. The probability that a cat is less than 3.8 kg is 0.0478 and the probability a cat is more than 4.2 kg is 0.1487. b. Find the mean and standard deviation of this distribution. Give your answers in kg correct to two decimal places. c. Twenty five of these cats are randomly selected. What is the probability that more than 20 of them will weigh between 3.8 and 4.2 kg? Give your answer correct to four decimal places. d. What is the least number of cats that would need to be sampled to ensure the probability that at least 21 of them will have weights between 3.8 and 4.2 kg is more than 0.95? The probability density function, s(x) for the number of hours a cat sleeps per day is given by 12 Sx S14 s(x) = a(x-16) +b 14