1. A small manufacturing company will start operating a night shift. There are 20 mechanists employed by the company. If a night crew consists of 3 mechanists, how many different crews are possible?
(A) 1140
(B) 6840
(C) 4913
(D) 5780
(E) not enough information to compute
(F) none of the above
2. A box contains 6 pens and 4 pencils. Two items are randomly selected simultaneously from this box. Find the probability that both selected items are pens.
(A) 16
(B) 13
(C) 23
(D) 124
(E) 112
(F) none of the above
3. How many different 8-letter codes can be formed by using all the letters of GOGOPAPA?
(A) 8!
(B) P4,8
(C) C4,8
(D) 8!4!
(E) 8!16
(F) none of the above
4. The simple mean x¯
(A) always lies in the middle class of the histogram
(B) is always the best measure of center
(C) is always the best measure of spread
(D) is always different from the sample median x˜
(E) is influenced by the outliers
(F) none of the above
5. Two fair dice are rolled simultaneously. Find the conditional probability P(sum is odd|sum is atmost 5)
(A) 35
(B) 25
(C) 15
(D) 310
(E) 110
(F) none of the above
6. The grade distribution of a large statistics class of 200 students was as follows: 21 received A grade, 32 received B grade, 98 received C grade, 30 received D grade, and 19 received F grade. Then the histogram of this date for the categorical variable 'grade':
(A) is strongly right skewed
(B) is strongly left skewed
(C) is unimodal
(D) is bimodal
(E) has an extreme outlier
(F) none of the above
7. Daily high temperatures (in Fahrenheit) recorded, in a Colorado town during first 7 days of March in a certain year, are as follows:
15 10 23 25 40 73 20 Find the five-number summary.
(A) (15, 10, 25, 73, 20)
(B) (10, 17.5, 25, 49, 73)
(C) (10, 17.5, 23, 32.5, 73)
(D) (10, 17.5, 23, 40, 73)
(E) not enough information to compute
(F) none of the above
8. Find the mild and extreme outliers of temperatures given in previous problem.
(A) 73 is the only extreme outlier
(B) 73 is the only mild outlier
(C) both 40 and 73 are mild outliers
(D) both 10 and 73 are extreme outliers
(E) there are no outliers
(F) none of the above
9. One can compute that the mean of 7 days high temperatures in problem (7) is 29.43°F (approximated to two decimal places). Find the sample mean, approximated to two decimal places, if the temperatures are measured in celcius (°C). Hint: C =59
F - 32.
(A) -15.65°C
(B) -3.43°C
(C) 4.20°C
(D) 3.43°C
(E) not enough information to compute
(F) none of the above
10. It is given that the standard deviation of 7 days high temperatures in problem (7) is 21.39°F (approximated to two decimal places). Find the sample standard deviation, approximated to two decimal places, if the temperatures are measured in celcius (°C).
(A) 11.88°C
(B) -20.12°C
(C) 3.05°C
(D) 20.12°C
(E) not enough information to compute
(F) none of the above
11. Each mortgage is classified as fixed rate (F) or variable rate (V). If four mortgages are randomly selected, find the probability that at most one of the four is a variable mortgage.
(A) 516
(B) 58
(C) 14
(D) 116
(E) 1116
(F) none of the above
12. If P(A) = 0.4, P(B) = 0.65, and P(A ∪ B) = 0.8, find P(A ∩ B).
(A) 0.2
(B) 0.25
(C) 0.6
(D) 0.35
(E) 0.4
(F) none of the above
13. If P(A) = 0.4, P(B) = 0.65, and P(A ∪ B) = 0.8, find P(A|B).
(A) 58
(B) 0.25
(C) 0.2
(D) 513
(E) not enough information to compute
(F) none of the above
14. If P(A) = 0.4, P(B) = 0.65, and P(A ∪ B) = 0.8, which one of the following is FALSE.
(A) P(B|A) = 58
(B) P(A0 ∩ B0) = 0.2
(C) P(A0 ∩ B) = 0.4
(D) P(A ∩ B0) = 0.15
(E) A and B are independent events
(F) A and B are not disjoint
15. If P(A ∪ B ∪ C) = 0.53, P(A) = 0.22, P(B) = 0.25, P(C) = 0.28, P(A ∩ B) = 0.11, P(B ∩ C) = 0.07, and P(A ∩ B ∩ C) = 0.01, find P(A ∩ C).
(A) 0.55
(B) 0.47
(C) 0.03
(D) 0.01
(E) 0.05
(F) none of the above
16. You randomly select 5 cards from a well shuffled deck of standard 52 cards. How many ways can you have at least 3 of them red cards?
(A) C3,26C2,26 + 26C4,26 + C5,26
(B) P3,26P2,26 + 26P4,26 + P5,26
(C) C3,26 + C4,26 + C5,26
(D) P3,26 + P4,26 + P5,26
(E) C3,52
C5,52
(F) none of the above
17. A little league team has 15 players and 5 of 15 players are left handed. Assume that each player can play in any position. If the coach randomly selects 9 players in an order (catcher, pitcher etc.,) for a game, find the probability that exactly 3 are left handed outfielders and all 6 other positions are occupied by right handed players.
(A) P3,5 P9,15
(B) P3,5P6,10 P9,15
(C) C3,5 C9,15
(D) C3,5C6,10 C9,15
(E) P3,9 P6,9
(F) none of the above
18. Suppose that a baseball coach randomly makes a list of batting order out of 9 players, 3 of whom are left handed. What is the probability that the first left handed player in the batting order is the third player?
(A) 23
(B) 13
(C) 528
(D) 59
(E) 3!9!
(F) none of the above
For next two problems, write all your steps clearly and write your answer as an exact simplified fraction (not as a decimal) on the front page;
19. At a certain gas station, 40% of the customers use regular gas, 35% use plus gas, and 25% use premium. Of those customers using regular gas, only 30% fill their tanks. Of those customers using plus, only 60% fill their tanks, whereas of those using premium, only 50% fill their tanks. If the next customer fills the tank, what is the probability that plus gas is requested?
20. A box contains 7 red balls, 2 yellow balls, and 1 green ball, which you cannot see inside the box. You are allowed to select two of the balls one after another without replacement. You win $20 for selecting the green ball and $5 for selecting a yellow ball and none for selecting a red ball. What is the probability that you win exactly $25? Show your steps below and enter your answer as an exact simplified fraction on the first page.