AP Statistics Multiple-Choice Practice Questions: Combining and Transforming Random Variables

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Question 7 questions

Time 16 minutes

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1. An auto dealer offers discounts averaging $2,450 with a standard deviation of $575. If 50 autos are sold during one month, what is the expected value and standard deviation for the total discounts given?

2. An auto dealer pays an average of $8,750 with a standard deviation of $1,200 for used car trade-ins, and sells new cars for an average of $28,500 with a standard deviation of $3,100. Assuming independence of trade-in and new car prices for a customer, what is the standard deviation of the revenue the dealer should expect to make if a customer trades in a used car and buys a new one?

3. Suppose a retailer knows that the mean number of broken eggs per carton is 0.3 with a standard deviation of 0.18. In a shipment of 100 cartons, what is the expected number of broken eggs and what is the standard deviation? Assume independence between cartons.

4. Science majors in college pay an average of $650 per year for books with a standard deviation of $130, whereas English majors pay an average of $465 per year for books with a standard deviation of $90. What is the mean difference and standard deviation between the amounts paid for books by science and English majors?

5. The auditor working for a veterinary clinic calculates that the mean annual cost of medical care for dogs is $98 with a standard deviation of $25 and that the mean annual cost of medical care for pets is $212 with an average deviation of $39 for owners who have one dog and one cat. Assuming expenses for dogs and cats are independent for those owning both a dog and a cat, what is the mean annual cost of medical care for cats, and what is the standard deviation?

6. A home theater projector system technician knows that based on past experience, for unpacking, assembly, and fine tuning, the mean total setup time is 5.6 hours with a standard deviation of 0.886 hours. The times for the three steps are independent, the mean and standard deviation for the unpacking time are 1.5 hours and 0.2 hours, and for the assembly time are 2.8 hours and 0.85 hours, respectively. What are the mean and standard deviation for the fine tuning time?

7. Boxes of 50 "donut holes" weigh an average of 16.0 ounces with a standard deviation of 0.245 ounces. If the empty boxes alone weigh an average of 1.0 ounce with a standard deviation of 0.2 ounces, what are the mean and standard deviation of donut hole weights?