The number of ants per acre in the forest is normally distributed with mean 44,000 and standard deviation 12,298. Let X = number of ants in a randomly selected acre of the forest. 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 acre in the forest has fewer than 53,951 ants. c. Find the probability that a randomly selected acre has between 43,197 and 55,069 ants. d. Find the first quartile. ants (round your answer to a whole number)

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Private nonprofit four-year colleges charge, on average, $26,161 per year in tuition and fees. The standard deviation is $7,190. 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 26,883 per year. c. Find the 76th percentile for this distribution. $ (Round to the nearest dollar.)

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The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 minutes and a standard deviation of 16 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 67 minutes. c. The park service is considering offering a discount for the 7% 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

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The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 minutes and a standard deviation of 16 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 67 minutes. c. The park service is considering offering a discount for the 7% 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

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