Close Enough
(77) Five managers and five employees are ona grievance committee. A three-person subcommittee is formed by a random selection from the ten committee members. What is the probability that all three members of the subcommittee are managers?
A. 1/12
B. 1/16
C. 3/16
D. 5/16
E. 1/2
A. 1/12
(47) Which of the following are unbiased estimators for the corresponding population parameters?
I. Sample means
II. Sample proportions
III. Difference of sample means
IV. Difference of sample proportions
A. None are unbiased
B. I and II
C. I and III
D. III and IV
E. All are unbiased
E. All are unbiased
(18) Box A has four $10 bills and single $100 bill, box B has 400 $10 bills and 100 $100 bills, and box C has 28 $1 bills. You can have all of box C or blindly pick one bill out of either box A or box B. Which choice offers the greatest expected winning?
A. Box A
B. Box B
C. Box C
D. Either A or B, but not C
E. All offer the same expected winning.
E. All offer the same expected winning.
(55) Which of the following statements is incorrect?
A. In all normal distributions, the mean and median are equal.
B. A normal distribution is completely determined by two numbers, its mean and its standard deviation.
C. All bell-shaped curves are normal distributions for some choice of mean and standard deviation.
D. Virtually all the area under a normal curve is within three standard deviations of the mean, no matter what the particular mean and standard deviation are.
E. Standardized scores (z-scores) have a normal distribution only if the original distribution is normal.
C. All bell-shaped curves are normal distributions for some choice of mean and standard deviation.
(41) The waiting time for a commuter bus is normally distributed with a mean of 8 minutes and a standard deviation of 2 minutes. If there are 3,000 riders a day, which of the following is the shortest time interval associated with 2,000 riders.
A. 0 to 8.9 minutes
B. 6.1 to 7.1 minutes
C. 6.1 to 8 minutes minutes
D. 6.1 to 9.9 minutes
E. 7.1 to 14 minutes
D. 6.1 to 9.9 minutes
(34) A basketball player makes one out of his first two free throws. From that point on, the probability that he makes the next shot is equal to the proportion of shots made up to that point. If he takes two more shots, what is the probability he ends up making a total of two free throws?
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
B. 1/3
(35) Which of the following is a true statement?
A. The area under the standard normal curve between 0 and 2 is twice the area between 0 and 1.
B. The area under the standard normal curve between 0 and 2 is half the area between -2 and 2.
C. For the standard normal curve, the interquartile range is approximately 3.
D. For the standard normal curve, approximately 1 out of 1000 values are greater than 10.
E. The 68-95-99.7 rule applies only to normal curves where the mean and standard deviation are known.
B. The area under the standard normal curve between 0 and 2 is half the area between -2 and 2.
(1) Review Book A advertises an average SAT gain of 40 points with a standard deviation of 12 points, and a Review Book B claims an average SAT gain of 35 points with a standard deviation of 15 points. Assuming both assertions are correct and assuming normal distributions, which review book is more likely to result in an SAT gain of over 60 points?
A. Review Book A because of its greater mean.
B. Review Book B because of its greater standard deviation.
C. For both plans, the probability of an SAT gain over 60 points is 0.04779.
D. For both plans, the probability of an SAT gain over 60 points is 0.95221
E. The problem cannot be solved from the information given.
C. For both plans, the probability of an SAT gain over 60 points is 0.04779.
(20) Which of the following statements is incorrect?
A. The larger the sample, the larger the spread in the sampling distribution.
B. Provided that the population size is significantly greater than the sample size, the spread of a sampling distribution is about the same no matter what the population size.
C. Bias has to do with the center, not the spread, of a sampling distribution.
D. Sample distribution and sampling distribution refer to different things.
E. The larger the sample, the closer the sample distribution generally becomes to the population distribution.
A. The larger the sample, the larger the spread in the sampling distribution.
(46) Suppose 56% of eight to twelve year olds expect to have a "great life." In an SRS 125 eight to twelve year olds, what is the probability that between 50 percent and 60 percent will say they expect to have a "great life"?
A. 0.2721
B. 0.5402
C. 0.6723
D. 0.7279
E. 0.8640
D. 0.7279
(19) There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between 45% and 55% heads; in the second game, you win if you can throw more than 60% heads. For each game, would you rather flip the coin 30 times or 300 times?
A. 30 times for each game
B. 300 times for each game
C. 30 times for the first game, and 300 for the second
D. 300 times for the first game, and 30 for the second
E. The outcomes of the games do not depend on the number of flips.
D. 300 times for the first game, and 30 for the second
(27) Suppose you toss a fair coin ten times and it comes up heads every time. Which of the following is a true statement?
A. By the Law of Large Numbers, the next toss is more likely to be tails than another heads.
B. By the properties of conditional probability, the next toss is more likely to be heads given that ten tosses ina row have been heads.
C. Coins actually do have memories, and thus what comes up on the next toss is influenced by the past tosses.
D. The Law of Large Numbers tells how many tosses will be necessary before the percentages of heads and tails are again in balance.
E. None of the above are true statements.
E. None of the above are true statements.
(17) There are five outcomes to an experiment and a stdent calculates the respective probabilities of the outcomes to be 0.34, 0.50, 0.42, 0.00, and -0.26. The proper conclusion is that
A. the sum of the individual probabilities is 1.
B. one of the outcomes will never occur.
C. one of the outcomes will occur 50% of the time.
D. all of the above are true.
E. the student made an error.
E. the student made an error.
(30) Which of the following statements is incorrect?
A. Like the normal, t-distributions are always unimodal.
B. Like the normal, t-distributions are always symmetric.
C. Like the normal, t-distributions are always bell-shaped.
D. The t-distributions have less spread than the normal; that is, they have less probability in the tails and more in the center than the normal.
E. For larger values of df, degrees of freedom, the t-distributions look more like the normal distribution.
D. The t-distributions have less spread than the normal; that is, they have less probability in the tails and more in the center than the normal.
(8) An insurance company charges $900 annually for auto policies for teenagers. The policy specifies the company will pay $1,500 for a minor accident and $8,000 for a major accident. If the probability of a minor accident during the year is 0.15, and of having a major accident is 0.05, how much can the insurance company expect to make on 10 policies?
A. $275
B. $625
C. $2,750
D. $6,250
E. $9,000
C. $2,750
(68) Three fair coins are tossed. If all land "heads," the player wins $10, and if exactly two land heads, the player wins $5. If it costs $4 to play, what is the player's expected outcome after four games?
A. Loss of $0.875
B. Loss of $1.00
C. Loss of $3.50
D. Win of $2.25
E. Win of $9.00
C. Loss of $3.50
(15) Which of the following are true statements?
I. The area under a normal curve is always equal to 1, no matter what the mean and standard deviation are.
II. The smaller the standard deviation of a normal curve, the higher and narrower the graph.
III. Normal curves with different means are centered around different numbers.
A. I and II
B. I and III
C. II and III
D. I, II, and III
E. None of the above fives the complete set of true responses.
D. I, II, and III
(2) Suppose that the probabilities that an answer can be found on Google is 0.95, on Answers.com is 0.92, and on both websites is 0.874. Are the possibilities of finding the answer on the two websites independent?
A. Yes, because (0.95)(0.92) = 0.874
B. No because (0.95)(0.92) = 0.874.
C. Yes, because 0.95 > 0.92 > 0.874.
D. No, because 0.5(0.95+0.92) =/= 0.874.
E. There is insufficient information to answer this question.
A. Yes, because (0.95)(0.92) = 0.874
(50) Which of the following statements is incorrect?
A. Sample statistics are used to make inferences about population parameters.
B. Statistics from smaller samples have more variability.
C. Parameters are fixed, while statistics vary depending on which sample is chosen.
D. As the sample size n becomes larger, the sample distribution becomes closer to a normal distribution.
E. All of the above are true statements.
D. As the sample size n becomes larger, the sample distribution becomes closer to a normal distribution.
There are 8,253 men and 10,327 women at a state university. If 43% of the men and 27% of the women are business majors, what is the expected number of business majors in a random sample of 200 students?
A. 31.7
B. 34.1
C. 63.4
D. 68.2
E. 70.0
D. 68.2
(32) Given the probabilities P(A) = 0.3 and P(A U B) = 0.7, what is the probability P(B) if A and B are mutually exclusive? If A and B are independent?
A. 0.4, 0.3
B. 0.4, 4/7
C. 4/7, 0.4
D. 0.7, 4/7
E. 0.7, 0.3
B. 0.4, 4/7
(5) Which of the following are true statements?
I. By the Law of Large Nubmers, the mean of a random variable will get closer and closer to a specific value.
II. The standard deviation of a random variable is never negative.
III. The standard deviation of a random variable is 0 only if the random variable takes a lone single value.
A. I and II
B. I and III
C. II and III.
D. I, ,II, and III
E. None of the above gives the complete set of true responses.
C. II and III.
(63) For which of the following is a binomial an appropriate model?
A. The number of heads in ten tosses of an unfair coin weighted so that heads comes up twice as often as tails.
B. The number of hits in give at-bats where the probability of a hit is either 0.352 or 0.324 depending upon whether the pitcher is right-handed or left-handed.
C. The number of tosses of a fair coin before heads appears on two consecutive tosses.
D. The number of snowy says in a given week.
E. The binomial is appropriate in all of the above.
A. The number of heads in ten tosses of an unfair coin weighted so that heads comes up twice as often as tails.
(57) Suppose two events, E and F, have nonzero probabilities p and q, respectively. Which of the following is impossible?
A. p + q > 1
B. p - q < 0
C. p/q > 1
D. E and F are neither independent nor mutually exclusive.
E. E and F are both independent and mutually exclusive.
E. E and F are both independent and mutually exclusive.
A. 0.0000
B. 0.0070
C. 0.0141
D. 0.3637
E. 0.9930
B. 0.0070