North Seattle Community College Winter 2011 ELEMENTARY STATISTICS 2617 MATH 109 - Section 05, Chapter 3 and 4 – Test 2 STUDENT NAME: __________________________ 13th February 2012 QUIZ SCORE: ______________________________ Question 1 (4 points) a. A shirt company has 4 designs each of which can be made with short or long sleeves. There are 7 color patterns available. How many different shirts are available from this company? b. If two-thirds of the books in the library are new, and half of the books in the library are non-fiction, but only one-third of the non-fiction books are new, find the probability that a book selected at random from the library is fiction, given that it is a new. Question 3 (7 points) A deck of cards has 52 cards with 4 queens. A gambling game consists of a player drawing three cards without replacement. The required bet is $10 i.e. you need $10 to buy into the game. The winnings depend on the number of queens drawn out of the three cards. If you get no queens you win $0, for 1 queen you receive $10, for 2 queens you can win 20 and for all queens you can win 500. 1. What is the probability distribution for number of queens drawn? 2. What would be the average gain? 3. What is the variance and standard deviation for the gain? Question 3 (4 point) You spin a number wheel that has 17 numbers 25 times. The random variable X represents the number of times you get 13 when you spin the wheel 25 times. a. What is the distribution of X ? b. What is the mean number of X? c. What is the standard deviation and variance of X? Question 4 (10 points) In the Venn diagram below, event A represents the adults who drink coffee, event B represents the adults who drink tea, and event C represents the adults who drink cola. Use the data in the diagram above to answer the following: a. What is the probability that an adult drinks all three cola, coffee and tea? b. What is the probability that an adult drinks only coffee? c. What is the probability that an adult does drinks none of the three? d. Are A, B and C mutually exclusive? Explain why? e. Are A, B and C independent? Explain why?