Suppose that the speed at which cars go on the freeway is normally distributed with mean 66 mph and standard deviation 6 miles per hour. Let X be the speed for a randomly selected car. a. What is the distribution of X? X ~ N(:],:]) b. If one car is randomly chosen, find the probability that it is traveling more than 67 mph. Round to 4 decumal places. [:] c. If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 69 mph. Round to 4 decimal places. C] The number of calories consumed by customers at the Chinese buffet is normally distributed with mean 2615 and standard deviation 664. 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 fewer than 2315 calories. C] c. What proportion of the customers consumed more than 3009 calories? C] Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 257 feet and a standard deviation of 35 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(:],:]) I). Find the probability that a randomly hit fly ball travels less than 256 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 Los Angeles workers have an average commute of 28 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. a. What is the distribution of X? X - N([:],[:]) b. Find the probability that a randomly selected LAworker has a commute that is longer than 34 minutes. Round to 4 decimal places. S c. Find the 90th percentile for the commute time of LAworkers. Round to 2 decimal places. C] minutes The average THC content of marijuana sold on the street is 9.3%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. a. What is the distribution of X? X - N(:],[:]) b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 7.4. Round to 4 decimal places. S c. Find the 61th percentile for this distribution. Round to 2 decimal places