# Statistic Question

1. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcome with probability 0.62. Create a new experiment consisting of repeating the original experiment 3 times. Assume each repetition is independent of the others. What is the probability of three successes?
A. 0.238
B. 0.055
C. 1.14
D. 0.762
2. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it’s short-haired?
Brown-haired Blond
Short-haired
0.06
0.23
Shaggy
0.51
0.20
A. 0.222
B. 0.0306
C. 0.06
D. 0.105
3. A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom. Find the probability that she’ll sell a car to exactly two of the next three customers.
A. 0.0071
B. 0.0075
C. 0.1354
D. 0.9939
4. Approximately how much of the total area under the normal curve will be in the interval spanning 2 standard deviations on either side of the mean?
A. 68.3%
B. 99.7%
C. 50%
D. 95.5%
5. Assume that an event A contains 10 observations and event B contains 15 observations. If the intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?
A. 10
B. 28
C. 0
D. 22
6. From an ordinary deck of 52 playing cards, one is selected at random. What is the probability that the selected card is either an ace, a queen, or a three?
A. 0.2308
B. 0.0769
C. 0.25
D. 0.3
7. An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector. What is the probability that both activating devices will work properly?
A. 0.965
B. 0.049
C. 0.9895
D. 0.931
8. Which of the following is correct concerning the Poisson distribution?
A. The mean is usually smaller than the variance.
B. The event being studied is restricted to a given span of time, space, or distance.
C. The mean is usually larger than the variance.
D. Each event being studied must be statistically dependent on the previous event.
Mark for review (Will be highlighted on the review page)
Protestant Catholic Jewish Other
Democrat
0.35
0.10
0.03
0.02
Republican
0.27
0.09
0.02
0.01
Independent
0.05
0.03
0.02
0.01
9. The table above gives the probabilities of combinations of religion and political parties in a city in the United States. What is the probability that a randomly selected person will be a Protestant and at the same time be a Democrat or a Republican?
A. 0.35
B. 0.89
C. 0.67
D. 0.62
10. A continuous probability distribution represents a random variable
A. having outcomes that occur in counting numbers.
B. that has a definite probability for the occurrence of a given integer.
C. that’s best described in a histogram.
D. having an infinite number of outcomes that may assume any number of values within an interval.
11. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of the following is correct concerning these two events?
A. On a Venn diagram, event A would overlap event B.
B. Events A and B are exhaustive.
C. On a Venn diagram, event B would contain event A.
D. Events A and B are mutually exclusive.
2. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Let A be the event “shaggy and brown-haired.” Compute P(Ac).
Brown-haired Blond
Short-haired
0.06
0.23
Shaggy
0.51
0.20
A. 0.49
B. 0.36
C. 0.51
D. 0.77
13. If event A and event B are mutually exclusive, P(A or B) =
A. P(A) + P(B) – P(A and B).
B. P(A + B).
C. P(A) – P(B).
D. P(A) + P(B).
14. Which of the following is a discrete random variable?
A. The time required to drive from Dallas to Denver
B. The number of three-point shots completed in a college basketball game
C. The weight of football players in the NFL
D. The average daily consumption of water in a household
15. Using the standard normal table in the textbook, determine the solution for P(0.00 ≤ z ≤ 2.01).
A. 0.4778
B. 0.0222
C. 0.1179
D. 0.4821
16. Find the z-score that determines that the area to the right of z is 0.8264.
A. 1.36
B. –0.94
C. 0.94
D. –1.36
17. The possible values of x in a certain continuous probability distribution consist of the infinite number of values between 1 and 20. Solve for P(x = 4).
A. 0.03
B. 0.05
C. 0.02
D. 0.00
18. What is the value of (8 over 5) ?
A. 336
B. 1.6
C. 6720
D. 56

19. Each football game begins with a coin toss in the presence of the captains from the two opposing teams. (The winner of the toss has the choice of goals or of kicking or receiving the first kickoff.) A particular football team is scheduled to play 10 games this season. Let x = the number of coin tosses that the team captain wins during the season. Using the appropriate table in your textbook, solve for P(4 ≤ x ≤ 8).
A. 0.377
B. 0.171
C. 0.817
D. 0.246

20. Tornadoes for January in Kansas average 3.2 per month. What is the probability that, next January, Kansas will experience exactly two tornadoes?
A. 0.1304
B. 0.2087
C. 0.2226
D. 0.4076

21. What is the purpose of sampling?
A. To create a point estimator of the population mean or proportion
B. To verify that the population is approximately normally distributed
C. To achieve a more accurate result than can be achieved by surveying the entire population
D. To estimate a target parameter of the population

22. For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of 98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of 2.75 pounds and a standard deviation of s = 14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the 0.05 level of significance?
A. We can conclude that we can’t reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.
B. We can conclude that the average cottage cheese consumption in America isn’t 2.6 pounds per person per year.
C. We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75 pounds per per11son per year.
D. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.

23. The power of a test is the probability of making a/an _______ decision when the null hypothesis is _______.
A. correct, true
B. correct, false
C. incorrect, true
D. incorrect, false

24. H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. One-tail testing of a mean
B. One-tail testing of a proportion
C. Two-tail testing of a proportion
D. Two-tail testing of a mean

25. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm’s employees?
A. 30
B. 3
C. 4
D. 2.5

26. What is the primary reason for applying a finite population correction coefficient?
A. If you don’t apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.
B. When the sample is a very small portion of the population, the correction coefficient is required.
C. If you don’t apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making.
D. If you don’t apply the correction coefficient, you won’t have values to plug in for all the variables in the confidence interval formula

27. If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she’ll perform _______-tail testing of a _______.
A. two, mean
B. one, proportion
C. one, mean
D. two, proportion

28. A portfolio manager was analyzing the price-earnings ratio for this year’s performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for the manager to use in this situation?
A. Because –2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20.
B. Because 2.81 is greater than 2.33, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20.
C. If t > 2.68 or if t < –2.68, reject H0.
D. If z > 2.33, reject H0.

29. What is the rejection region for a two-tailed test when α = 0.05?
A. |z | > 1.96
B. |z | > 2.575
C. |z | > 1.645
D. z > 2.575

30. A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence interval estimate if there are 30 applicants in the group.
A. 63.14 to 85.26
B. 13.64 to 134.76
C. 68.72 to 79.68
D. 64.92 to 83.48

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