Questions
1. Assume a sample has been selected at random from a large population. Which of the following five statements is correct.
A. The standard error equals the standard deviation of the sample mean.
B. The sample standard deviation decreases by one if the value one is subtracted from each sample unit.
C. If each sample unit is multiplied by the number 2, then the sample standard deviation will increase by the square-root of 2.
D. If all sample units are equal to each other, then the standard error will be the number 1.
E. The standard error increases as the sample size increases.
2. A golfer is approaching the fourteenth hole, and he has 2 par-three holes and 3 par-four holes remaining in the match. He knows from experience that he stands a 60% chance of making par or better on each of the par-three holes and a 75% chance of making par or better on each of the par-four hole. What's the probability that he'll shoot par or better on at least four of the last five holes?
A. 0.25
B. 0.69625
C. 0.50625
D. 0.151875
E. 0.30375
3.In a game of dice at a Nevada state fair, a player pays $10 to roll a pair of fair dice. If the two dice rolled sums to 2, the house pays $40. If the two dice rolled sums to 3, the house pays $30. If the two dice rolled sums to 4, the house pays $20. If the two dice rolled sums to 5, the house pays $10. If the two dice rolled sums to a number greater than 5, the house pays nothing.
On average, what can the house expect to receive for each roll of the dice? (Round to the nearest penny.)
A. House wins an average of $4.44 for each roll.
B. House loses an average of $2.22 for each roll.
C. House wins an average of $5.56 cents for each roll.
D. House wins an average of $3.89 for each roll.
E. House wins an average of 28 cents for each roll.
4.Rod has taken his bar exam to begin practicing as an attorney. He was informed that he placed in the 86th percentile. Scores for the bar exam were normally distributed with a mean of 177 and a standard deviation of 38. What score did he receive?
A. 199
B. 218
C. 233
D. 246
E. 254
5.David scored 78 on a statistics mid-term that he had taken. The scores were normally distributed, and based on a table posted by the instructor for the class, his score corresponded to a Z-Score of 1.15. David's friend Scott received a score of 92 on the same mid-term, and his score corresponded to a Z-Score of 1.85. What was the standard deviation of all the scores?
A. 7
B. 14
C. 17
D. 20
E. 23
6.Two fair dice are thrown. Let P be the probability that the product (multiply) of the two die will exceed some number. Which of the following probabilities is not possible for the value of P? Assume that all probabilities are rounded to the nearest ten-thousandth. (HINT: Order the products from largest to smallest for all possible rolls of the die.)
A. 0.2222
B. 0.1667
C. 0.7778
D. 0.5556
E. 0.4167
7.Suppose that A, B, and C are all independent, mutually exclusive events. Which of the following is the probability of events A or B occurring at the same time that event C occurs?
A. [ Pr(C) - Pr(A) ] x [ Pr(C) - Pr(B) ]
B. [ Pr(A) x Pr(B) ] + Pr(C)
C. 1
D. [Pr(A) x ( 1-Pr(C) )] + [Pr(B) x ( 1-Pr(C) )]
E. Pr(C) x [ Pr(A) + Pr(B) ]
8.In the 1940's, physicians noticed that there might be an association between kidney disease and diabetes. To determine if an association existed, they could use two sampling plans:
Plan A: Select 500 people at random who have diabetes and 500 people at random who do not have diabetes. Compare the proportion of people with kidney disease among diabetics with the proportion of people with kidney disease among non-diabetics.
Plan B: Select 1000 people at random and compare the percent of diabetics with kidney disease with the proportion of non-diabetics with kidney disease.
Which of the following statements is the most correct in how the investigators should approach their goal?
A. Choose Plan A over Plan B.
B. Choose Plan B over Plan A.
C. Both plans are equally capable of addressing their intended goal.
D. Neither plan can be used to address the intended goal.
E. The plans can't be evaluated based on the information provided.