PLEASE I REALLY NEED HELP

(1) The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 34 and a standard deviation of 10. 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 that a randomly selected fat calorie percent is more than 36. c. Find the minimum number for the upper quarter of percent of fat calories.

(2) Americans receive an average of 19 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 7. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. If an American is randomly chosen, find the probability that this American will receive no more than 23 Christmas cards this year. c. If an American is randomly chosen, find the probability that this American will receive between 20 and 26 Christmas cards this year. d. 63% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

(3) The average American man consumes 10 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that this American man consumes between 10.9 and 12.8 grams of sodium per day. c. The middle 30% of American men consume between what two weights of sodium? Low: High:

(4) Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 263 feet and a standard deviation of 42 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly hit fly ball travels less than 290 feet. Round to 4 decimal places. c. Find the 90th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feet

(5) According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that the person is between 64.7 and 67.4 inches. c. The middle 30% of Martian heights lie between what two numbers? Low: inches High: inches

(6) Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 5 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. If one of the trials is randomly chosen, find the probability that it lasted at least 23 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 25 and 30 days. d. 74% of all of these types of trials are completed within how many days? (Please enter a whole number)

(7) On average, indoor cats live to 16 years old with a standard deviation of 2.5 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 ~ N(,) b. Find the probability that an indoor cat dies when it is between 13.3 and 15.3 years old. c. The middle 40% of indoor cats' age of death lies between what two numbers? Low: years High: years

(8) The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 80 minutes and a standard deviation of 15 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected person at the hot springs stays longer then 75 minutes. c. The park service is considering offering a discount for the 6% 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. Q1: minutes Q3: minutes IQR: minutes

(9) Private nonprofit four-year colleges charge, on average, $27,917 per year in tuition and fees. The standard deviation is $7,376. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 23,966 per year. c. Find the 70th percentile for this distribution. $ (Round to the nearest dollar.)

(10) Suppose that the speed at which cars go on the freeway is normally distributed with mean 65 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. 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 62 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 64 and 69 mph. d. 82% of all cars travel at least how fast on the freeway? mph.

(11) On the planet of Mercury, 4-year-olds average 2.9 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that the child spends less than 2.2 hours per day unsupervised. c. What percent of the children spend over 4.8 hours per day unsupervised. % (Round to 2 decimal places) d. 69% of all children spend at least how many hours per day unsupervised? hours.

(12) The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2965 and standard deviation 508. 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 2793 calories. c. What proportion of the customers consume over 3295 calories? d. The Piggy award will given out to the 3% 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)

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