BUSINESS STATISTICS 271 Practice Test - Sets & Counting Rules NAME_____________________ DATE__________ ______ 1. A firm interviews sixteen applicants for a position on its sales force. One question on the application form concerns leisure-time activities. Seven applicants say they spend a major portion of their leisure time playing golf. Ten applicants spend time bowling. Four do not mention sports at all. How many applicants spend their leisure time both golfing and bowling? Illustrate with a Venn diagram. (HINT: n(AB) = n(A) + n(B) - n(AB) 2. A final exam consists of thirty possible questions. A student is told to omit any five questions. How many possible tests can be constructed under these conditions? (HINT: Rearranged questions do not constitute a new test.) 3. Car tags in a certain state can have three letters followed by three numbers (ex: JFW - 899 or ABC -123, etc). If each car in the state must have its own separate number, how many tags can the state issue? (HINT: Letters and numbers may be used more than once.) 4. From the problem above, how many tags would be possible if the state allowed letters and numbers to appear in any sequence, but allowed each number or letter to be used only once (ex: 9J87FW or F8JW79)? 5. Six women and five men enter a classroom. There are desks numbered one through eleven along the back wall. They must be seated at the desks in such a way that the women are always in the odd numbered seats and the men are always in the even numbered seats. How many different seating arrangements are possible? 6. If we use the numbers 0 through 9, how many distinct 3 digit numbers can we create if: (A) each number can be used more than once, (B) each number may be used only once? 7. Consider the following purchases of a raw material for a certain manufacturing process. What was the average price paid per pound for the raw material? Date of Purchase 02-02-06 03-14-06 05-20-06 06-29-06 08-08-06 10-14-06 8. Price per Pound 1.25 1.35 1.20 1.45 .99 1.18 Amount Purchased 25 30 40 10 60 35 What are the mean, variance and standard deviation of the following grouped data? Age Range Number 0-9 10 - 19 20 - 29 30 - 39 40 - 49 5 8 10 7 3