PRINTABLE VERSION Practice Test 4 Question 1 Given P(Ec ) = 0.45, P(F) = 0.54, and P(E F) = 0.18. Find P( E | Fc ). a) 0.5068 b) 0.8222 c) 0.6851 d) 0.3333 e) 0.8043 f) None of the above. Question 2 Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the first card drawn is a 2 and the second card drawn is a 3? a) 0.0059 b) 0.1569 c) 0.1554 d) 0.0045 e) 0.0060 f) None of the above. Question 3 A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even? a) 0.3667 b) 0.2778 c) 0.1389 d) 0.4545 e) 0.3056 f) None of the above. Question 4 10 black balls and 7 white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball? a) 0.2316 b) 0.2574 c) 0.3875 d) 0.4118 e) 0.1544 f) None of the above. Question 5 There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 9 chocolate chip and 12 sugar cookies. The green jar contains 13 chocolate chip, 10 sugar and 14 peanut butter cookies. The pink jar contains 7 chocolate chip, 5 sugar and 8 peanut butter cookies. One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are 1/2, 1/4, and 1/4 respectively. A cookie is then chosen at random from the chosen jar. What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie? a) 0.2290 b) 0.0625 c) 0.0833 d) 0.1503 e) 0.2500 f) None of the above. Question 6 John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year. Number of Lease Offices 0 1 2 3 4 5 Probability 2/7 3/35 6/35 1/7 9/35 2/35 If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars) a) E(X) = $26,067.14 b) E(X) = $25,987.14 c) E(X) = $26,157.14 d) E(X) = $26,057.14 e) E(X) = $26,087.14 f) None of the above. Question 7 A probability distribution has a mean of 28 and a standard deviation of 4. Use Chebychev's inequality to estimate the probability that an outcome of the experiment lies between 17 and 39. a) 0.1322 b) 0.3636 c) 0.8678 d) 0.0204 e) 0.9796 f) None of the above. Question 8 A local amateur ice skater estimates that the probability she will place first in the next regional competition is 0.60. What are the odds she will win this competition? a) 3 to 2 b) 7 to 3 c) 3 to 8 d) 2 to 3 e) 8 to 3 f) None of the above. Question 9 The probability distribution of a random variable X is given below. x 3 4 6 7 9 P(X = x) 10/29 2/29 6/29 4/29 7/29 Given the following mean Find the variance (Var(X)) and the standard deviation, respectively. a) [5.59, 2.37] b) [1101.00, 33.18] c) [1828.91, 42.77] d) [22.86, 4.78] e) [44.92, 6.70] f) None of the above. Question 10 Consider the following Binomial Experiment: The probability that a cell phone manufactured at Electronics Unlimited is defective is 0.11. If a sample of 9 cell phones is selected at random, what is the probability that at least one is defective? a) 0.3504 b) 0.6496 c) 0.3118 d) 0.3937 e) 0.6063 f) None of the above. Question 11 Consider the following binomial experiment: A survey shows 79% of households in Centercity own a DVD player. In a random sample of 17 households in this city, what is the probability that exactly 9 households own a DVD player? a) 0.0110 b) 0.0114 c) 0.0106 d) 0.0111 e) 0.0108 f) None of the above. Question 12 Consider the following binomial experiment: A newspaper publisher claims that 53% of the people in a certain community read his newspaper. Doubting the assertion, a competitor randomly surveys 274 people in the community. Find the standard deviation of this experiment, if the newspaper publisher's claim is correct. a) 7.9616 b) 8.2616 c) 8.3616 d) 8.6616 e) 8.5616 f) None of the above. Question 13 Let Z be a standard normal variable. Find P(Z < 0.19). a) 0.5398 b) 0.4602 c) 0.4247 d) 0.5753 e) 0.5793 f) None of the above. Question 14 Let Z be a standard normal variable. Find P(-0.86 < Z < 2.25). a) 0.1980 b) 0.7898 c) 0.7929 d) 0.7884 e) 0.7742 f) None of the above. Question 15 Let Z be a standard normal variable. Find the value of z if z satisfies P( -z < Z < z) = 0.8788. a) 1.17 b) -1.10 c) 1.54 d) 1.50 e) 1.55 f) None of the above. Question 16 Let Z be a standard normal variable. Find the value of z if z satisfies P(Z > z) = 0.0020. a) -2.80 b) 2.88 c) 2.80 d) -3.00 e) -2.74 f) None of the above. Question 17 Suppose X is a normal random variable with and Find P(13.7 < X < 30.7). a) b) c) d) e) f) None of the above. Question 18 Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of 18.8 days and a standard deviation of 2 days. Find the probability that a butterfly will live between 17.04 and 19.32 days. a) 0.2088 b) 0.2080 c) 0.4065 d) 0.4132 e) 0.3674 f) None of the above. Question 19 Use the normal distribution to approximate the following binomial distribution. You claim that 73% of the voters in your district will vote for you. 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