The average amount of money spent for lunch per person in the college cafeteria is $6.89 and the standard deviation is $2.53. Suppose that 45 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.0842 and $7.3228.  For the group of 45 patrons, find the probability that the average lunch cost is between $7.0842 and $7.3228. (           ) For part d), is the assumption that the distribution is normal necessary? NoYes

Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 7 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 67 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 74 and 77 mph. d. 83% of all cars travel at least how fast on the freeway?  mph.

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 71 minutes and a standard deviation of 17 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 90 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

The average THC content of marijuana sold on the street is 9.4%. Suppose the THC content is normally distributed with standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible, a.  What is the distribution of X? X ~ N(Correct,Correct) b.  Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.7. c.  Find the 67th percentile for this distribution. %