The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 76 minutes and a standard deviation of 14 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 80 minutes. c. The park service is considering offering a discount for the 4% 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

Private nonprofit four-year colleges charge, on average, $26,317 per year in tuition and fees. The standard deviation is $7,323. 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 28,531 per year. c. Find the 66th percentile for this distribution. $ (Round to the nearest dollar.)

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 111 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected person's IQ is over 117. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2747 and standard deviation 515. 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 2352 calories. c. What proportion of the customers consume over 2961 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)

In the 1992 presidential election, Alaska's 40 election districts averaged 1930 votes per district for President Clinton. The standard deviation was 572. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = 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? X ~ N(,) b. Is 1930 a population mean or a sample mean? Select an answer Sample Mean Population Mean c. Find the probability that a randomly selected district had fewer than 1767 votes for President Clinton. d. Find the probability that a randomly selected district had between 2105 and 2306 votes for President Clinton. e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.