Math 118 Sections 3 & 13 Practice Exam 1

Math 118 Practice Final

Closed book & notes except one 8.5x11-inch sheet of paper; front and back may be used. Bring your calculator!

THIS PRACTICE TEST DOES NOT INCLUDE EVERY TOPIC THAT MIGHT BE ON THE REAL TEST!

A good way to study is to make a list of all the types of problems we’ve talked about (in class, worksheets, the textbook, homeworks, and projects) and make sure you know how to do each type, and understand the connections between them.

Exam is:

9am section: Monday Dec. 15th at 9am

10am section: Friday Dec. 12th at 9:30am NOTE THE HALF-HOUR EARLY!

The allotted exam time is 90 minutes.

#1 The probability that someone in Afghanistan has TB (tuberculosis) is 661/10,000. A simple tuberculosis test has a true-negative probability of 99% and a true-positive probability of 98%. If someone in Afghanistan tests positive, what is the probability that they actually have TB?

(for your information, not for use in Problem #1: the TB rate in the US is 4/10,000 instead of 661/10,000)

#2 Consider the following data on student performance on Exam 1 and Exam 2 (not in our Math 118 classes, though):

(a)What is the best average prediction of the Exam 2 score of someone who scored a 90 on Exam 1? Give three decimal places, even though we know their score will be an integer.

(b)How much do you believe this prediction? Give both a quantitative and a qualitative answer.

#3 a) When you solve a linear program, will your solution often have a bit of wiggle room in it before it becomes infeasible, or will it usually be hard up against the constraints? Explain.

b) If you have two things you want to do, like minimize risk and maximize return, can you have two objective functions in the linear program? Explain.

c) If you try to solve a linear program and Excel says it’s infeasible, does that mean you made a mistake? Explain.

d) If you solve an LP, then add a constraint and re-solve, explain what could or will happen to the new objective function value.

#4 Suppose that a crash costs a car insurance company $40,000, and they’ll drop you after you have 1 accident, so the number of times they’d pay out on you is either zero or once. They charge you $500 per year. What does this mean about their probability that you will have a crash this year? Give an exact number.

#5 The price of electricity two years ago (2006) was 8 cents per kiloWatt-hour (kWh), and now (2008) it is 9 cents per kWh. Using a linear model, predict the price in 2011.

#6 Use what you’ve learned on the swimsuit project to answer this question. If you often buy a perishable item (e.g. fresh donuts) and it has been your experience that the bakery is never out-of-stock, what does that mean about the retail price compared to the “wholesale” price (the bakery’s cost to make the donuts)?

#7 Market forecasts predict that a particular new car would sell 100,000 units at a price of $15,000 and 80,000 units at a price of $20,000.

(a)Using a linear model, predict the sales at a price of $22,000

(b)Of those three prices, which one brings in the most revenue?

#8 Consider the following data on family sizes (it excludes couples with no children)

(a)Make a histogram of this data.

(b)Compute the average number of children per family for this data set, down to 3 decimal digits (hint: it is not the classic “2.5”)

(c)What is the probability of a family having 3 or fewer children?

#9 A common sentiment among people who play slot machines is: “this one hasn’t paid out in the last 150 pulls, and its posted payout probability is 1/80, so it’s due; I’ll just play a few more times.” Write a sentence or two responding to this, based on what we’ve learned in class.

#10 If you want an LP to have an integer solution, can you just round your results? Circle one. Partial credit will be given for reasoning shown, if needed.

(a) yes, you can always just round

(b) no, you can never get away with rounding

(c) it’s usually okay to round if the variables are small

(d) it’s usually okay to round if the variables are large