The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 74 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 88 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

2.The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.5 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(______,_________)

b. What is the median recovery time?________days

c. What is the Z-score for a patient that took 5.7 days to recover?____________

d. What is the probability of spending more than 4.1 days in recovery?__________

e. What is the probability of spending between 4.4 and 5.3 days in recovery?_________

f. The 75th percentile for recovery times is __________days.

3.Terri Vogel, an amateur motorcycle racer, averages 129.77 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.29 seconds . The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(_______,___________)

b. Find the proportion of her laps that are completed between 129.24 and 130.96 seconds.________

c. The fastest 2% of laps are under________ seconds.

d. The middle 40% of her laps are fromseconds to__________seconds.

4.Americans receive an average of 22 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 8. 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 20 Christmas cards this year.__________

c. If an American is randomly chosen, find the probability that this American will receive between 21 and 25 Christmas cards this year.___________

d. 85% of all Americans receive at most how many Christmas cards? (Please enter a whole number)________

5.The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. 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 with a kidney stone will take longer than 9 days to pass it._________

c. Find the minimum number for the upper quarter of the time to pass a kidney stone._____days.

6.Private nonprofit four-year colleges charge, on average, $26,232 per year in tuition and fees. The standard deviation is $7,066. 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 22,395 per year._________

c. Find the 69th percentile for this distribution. $ ________(Round to the nearest dollar.)