Los Angeles workers have an average commute of 34 minutes. Suppose the LA commute time is normally distributed with a standard deviation of13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible. a. What is the distribution of X? it ~ Ni || 1 b. Find the probability that a randomly.r selected LAworker has a commute that is longer than 33 minutes. c. Find the ?5th percentile for the commute time of Lworkers. minutes The percent of fat calories that a person in America consumes each day is normally-r distributed 1with a mean of about 33 and a standard deviation of '5'. Suppose that one individual is randomly chosen. Let X=percent of fat calories. Round all answers to 4 decimal places if where possible a. What is the distribution of X? X ~ N{ b. Find the probability.r that a randomly selected fat calorie percent is more than 43.| | c. Find the minimum number for the upper quarter of percent of fat calories. I I Suppose that the distance of fly.r balls hit to the outfield {in baseball] is normally distributed with a mean of 269 feet and a standard deviation of 40 feet. Let 3'; be the distance in feet for a fly.r ball. a. What is the distribution of X? it ~ Ni || 1. in. Find the probability that a randomly.r hit fl}...r ball travels less than 319 feet. Round to 4 decimal places. c. Find the 80th percentile for the distribution of distance of fly balls. Round to 2 decimal places. I lfeet The amount of time that people spend at lEiroirer Hot Springs is normally.r distributed with a mean of 68 minutes and a standard deviation of 16 minutes. Suppose one person at the hot spn'ngs is randomly chosen. Let K = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. what it the distribution of K? it ~ M || 3 b. Find the probability that a randomly.r selected person at the hot springs stays longer then 1'2 minutes. c. The park service is considering offering a discount for the se of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount?| minutes. d. Find the Inter Quartile Range [IQR] for time spent at the hot springs. [11: I Iniinutes [13: I lniinutes IQR: I I minutes In the 1992 presidential election, Alaska's 48 election districts averaged 1842 votes per district for President Clinton. The standard deviation was 588. [There are only 48 election districts in Masha] The distribution of the votes per district for President Clinton was bell-shaped. Let I = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts} Round all answers except part e. to 4 decimal places. a. What is the distribution of X? I ~ N|{| I: b. Is 1842 a population mean or a sample mean? c. Find the probability that a randomly selected district had fewer than 1228 votes for President Clinton. d. Find the probability that a randomly selected district had between 19?? and 2258 votes for President Clinton. I | e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number. 6 The mean height of an adult giraffe is 17 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the median giraffe height? ft. c. What is the Z-score for a giraffe that is 20 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 17.4 feet tall? e. What is the probability that a randomly selected giraffe will be between 18 and 18.6 feet tall? f. The 80th percentile for the height of giraffes is ft