1. A random sample of two obrvations is taken from a population that is normally distributed with a mean of 100 and a standard deviation of 5. Which of the following is clost to the probability that the sum of the two obrvations is greater than 221？
A. 0.0015
B. 0.0250
C. 0.0500
D. 0.4500
E. 0.9985
Answer ：A
Analysis ：本题考查正态变量大于某个数的概率。P(X>221) = P(Z>24.2) = 0.0015
2. Let X reprent a random variable who distribution is normal, with a mean of 100 and a standard deviation of 10. Which of the following is equivalent to P(X >115)?
A. P(x < 115)
B. P(x <= 115)
C. P(x < 85)
D. P(85 < x < 115)
E. 1 - P(x < 85) Answer ：C
Analysis ：本题考查正态分布的对称性。均值为100，那么和115对称的就是100-15 = 85。
3. Suppo that public opinion in a large city is 65 percent in favor of increasing taxes to support the public school system and 35 percent against such an increa. If a random sample of 500 people from this city are interviewed, what is the approximate probability that more than 200 of the people will be against increasing taxes?
A.200300500(0.65)(0.35)200⎛⎫ ⎪⎝⎭
B.200300500(0.35)(0.65)200⎛⎫ ⎪⎝⎭
C.P z ⎛⎫
⎪ > ⎝
D.P z ⎛⎫ ⎪ > ⎝
E.P z ⎛⎫
⎪ > ⎝
Answer ：E Analysis ：本题考查二项用正态模拟。
4. A summer resort rents rowboats to customers but does not allow more than four people to a boat.
Each boat is designed to hold no more than 800 pounds. Suppo the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual pasngers are independent, what is the probability that a group of four adult male pasngers will exceed the acceptable weight limit of 800 pounds?
A. 0.023
B. 0.046
C. 0.159
D. 0.317
E. 0.977
Answer ：A
Analysis ：本题考查正态概率的计算，是综合题。首先要知道4个人坐船后总重量的分布，每个人的重量服从均值为190pounds 、标准差为10pounds 的正态分布。4个人的总重量则服从均值为190 * 4 =
760pounds 、方差为4 * 100 = 400 的正态分布。现在要计算4个人的总重量大于800pounds 的概率，P(X > 800) = P(Z > 80076020
-) = 0.023 5. An urn contains exactly three balls numbered 1, 2, and 3, respectively. Random samples of two balls are drawn from the urn with replacement. The average, 122X X X +=
, where X 1 and X 2 are the numbers on the lected balls, is recorded after each drawing. Which of the following describes the sampling distribution of X ?
A.
D.
E. It cannot be determined from the information given
Answer B
Analysis ：本题考查抽样分布的概念。122
X X X +=，其取值分别为：1, 1.5, 2, 2.5, 3。 6. A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 conds with a standard deviation of 16.0 conds. Suppo the reported values are the true mean and standard deviation for the population of subjects in the study . If a random sample of 144 subjects is lected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 conds?
A. 0.1151
B. 0.2743
C. 0.7257
D. 0.8849
E. Bad on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated. Answer ：C
Analysis ：本题考查样本均值抽样分布的概率计算。P(X > 11.0) = 1 - P( Z <
) 7. A volunteer for a mayoral candidate’s campaign periodically conducts polls to estimate the proportion of people in the city who are planning to vote for this candidate in the upcoming election. Two weeks before the election, the volunteer plans to double the sample size in the polls. The main purpo of this is to
A. reduce nonrespon bias
B. reduce the effects of confounding variables
C. reduce bias due to the interviewer effect
D. decrea the variability in the population
E. decrea the standard deviation of the sampling distribution of the sample proportion Answer ：E
Analysis ：本题考查抽样分布的标准差和样本容量的关系。样本容量增大抽样分布的标准
差减小。
8.
The graphs of the sampling distributions, I and II, of the sample mean of the same random variable f
or samples of two different sizes are shown above. Which of the following statements must be true about the sample size?
A. The sample size of I is less than the sample size of II.
B. The sample size of I is greater than the sample size of II.
C. The sample size of I is equal to the sample size of II.
D. The sample size does not affect the sampling distribution.
E. The sample size cannot be compared bad on the graphs.
Answer：B
Analysis：本题考查样本均值抽样分布的方差受样本容量影响。
9. A rearcher has conducted a survey using a simple random sample of 50 registered voters to create a confidence interval to estimate the proportion of registered voters favoring the election of a certain candidate for mayor. Assume that the sample proportion does not change. Which of the follo
wing best describes the anticipated effect on the width of the confidence interval if the rearcher were to survey a random sample of 200, rather than 50, registered voters.
A. The width of the new interval would be about one-fourth the width of the original interval
B. The width of the new interval would be about one-half the width of the original interval.
C. The width of the new interval would be about the same as the width of the original interval.
D. The width of the new interval would be about twice the width of the original interval.
E. The width of the new interval would be about four times the width of the original interval. Answer ：B
Analysis ：本题考查区间半径受什么影响。这里是比例的置信区间，E z α=在其他变量不变的情况下，样本容量n 由50变为200，区间半径变为原来的1/2。
10. Ten students were randomly lected from a high school to take part in a program designed to ra
i their reading comprehension. Each student took a test before and after completing the program. The mean of the differences between the score after the program and the score before the program is 16. It was decided that all students in the school would take part in this program during the next school year. Let A μ denote the mean score after the program and B μ denote the mean score before the program for all students in the school. The 95 percent confidence interval estimate of the true mean difference for all students is (9, 23). Which of the following statements is a correct interpretation of this confidence interval?
A.
A μ>
B μwith probability 0.95. B.
A μ<
B μwith probability 0.95 C. A μis around 23 and B μis around 9.
D. For any A μand B μwith A B μμ-≥14, the sample result is quite likely.
E. For any A μand B μwith 9 <A B μμ- < 23, the sample result is quite likely.
Answer ：E
Analysis ：本题考查置信区间的含义。A B μμ-的95%的置信区间为(9, 23)，意味着所有A B μμ-可能样本中，有95%的样本包含A B μμ-的真实值，所以(9, 23)很有可能包含A B μμ-。
11. A simple random sample produces a sample mean,x , of 15. A 95 percent confidence interval for the corresponding population mean is 15 ± 3. Which of the following statements must be true?
A. Ninety-five percent of the population measurements fall between 12 and 18.
B. Ninety-five percent of the sample measurements fall between 12 and 18.
C. If 100 samples were taken, 95 of the sample means would fall between 12 and 18.
