Mathematics

Problem 1: The average Saturday attendance at a movie theater is 974 people with a standard deviation of 54 people.
Part A: What is the probability that less than 900 people will attend this coming Saturday? (2 pts)

Part B: What is the probability of between 875 and 1075 people will attend this Saturday? (2 pts)

Part C: Eighty percent of Saturday attendances will be less than how many people? (2 pts)

Part D: The movie theater manager wants to determine a staffing level such that 98% of the time she can service the customers. How many customers should she set a staffing plan to serve? (2 pts

Problem 2: The average Saturday attendance at a movie theater is 974 people with a standard deviation of 54 people. A random sample of 39 Saturdays is selected.
Part A: What is the probability that a sample mean will be either less than 954 people or greater than 970 people? (2 pts)

Part B: There is a 97% chance that a sample mean will be above what attendance level? (2 pts)

Problem 3: What is the probability that more than 1000 people will attend the theater this Saturday? (2 pts)

Problem 4: The mean weight of hogs at a hog barn is 656 pounds with a standard deviation of 43 pounds.
Part A: What is the probability that a hog will weigh more than 700 pounds? (2 pts)

Part B: What is the probability that a hog will weigh either less than 590 pounds or more than 670 pounds? (2 pts)

Part C: Sixty-five percent of hogs will weigh more than what weight? (2 pts)

Problem 5: The mean weight of hogs at a hog barn is 656 pounds with a standard deviation of 43 pounds. A random sample of 43 hogs is selected.
Part A: What is the probability that a sample mean will be between 650 and 660 pounds? (2 pts)

Part B: There is a 70% chance that a sample mean will be below what weight? (2 pts)

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