The average amount of money spent for lunch per person in the college cafeteria is $7.39 and the standard deviation is $2.94. Suppose that 41 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible a. What is the distribution of X? X~ N(7.39 b. What is the distribution of ? a~ N(] c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.7112 and $8.2708 d. For the group of 41 patrons, find the probability that the average lunch cost is between $7.7112 and $8.2708 2.94 Yes ONo e. For part d), is the assumption that the distribution is normal necessary? Hint:

D, e, f and h

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 60 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 81 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

he mean height of an adult giraffe is 18 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 18.2 feet tall? e. What is the probability that a randomly selected giraffe will be between 18.9 and 19.6 feet tall? f. The 70th percentile for the height of giraffes is  ft.