On average, indoor cats live to 15 years old with a standard deviation of 2.7 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible. a. What is the distribution of X? X Nd |,| ) b. Find the probability that an indoor cat dies when it is between 14.7 and 18.3 years old. c. The middle 30% of indoor cats' age of death lies between what two numbers? Low: | |years High: 1 | years The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2612 and standard deviation 551. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? x - N(! |) b. Find the probability that the customer consumes less than 2395 calories. | | c. What proportion of the customers consume over 2986 calories?\" | d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? | calories. (Round to the nearest calorie) Suppose that the distance of fly balls hit to the outfield (in baseball} is normally distributed with a mean of 255 feet and a standard deviation of 43 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ Nd ' |) b. Find the probability that a randomly hit fly ball travels less than 272 feet. Round to 4 decimal places. c. Find the 85th percentile for the distribution of distance of fly balls. Round to 2 decimal places. | | feet The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. What is the distribution of X? x ~ Nil 1! i) b. Find th_e probability that a randomly selected person with a kidney stone will take longer than 18 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days