# Statistics MCQs – Discrete Distributions Part 2

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21. A study conducted at a certain university shows that 45 % of the university՚s graduates obtain a job in their chosen field within one year after graduation. 15 graduates are selected at the university at random one year after graduation. What is the probability that exactly 7 of them will have found a job in their chosen field?

a. 0.201

b. 0.051

c. 0.078

d. 0.165

e. 0.140

Answer: A

22. A study conducted at a certain university shows that 45 % of the university՚s graduates obtain a job in their chosen field within one year after graduation. 15 graduates are selected at the university at random one year after graduation. What is the probability that exactly 10 of them will have found a job in their chosen field?

a. 0.201

b. 0.051

c. 0.078

d. 0.165

e. 0.140

Answer: B

23. A study conducted at a certain university shows that 45 % of the university՚s graduates obtain a job in their chosen field within one year after graduation. 15 graduates are selected at the university at random one year after graduation. What is the probability that exactly 4 of them will have found a job in their chosen field?

a. 0.201

b. 0.051

c. 0.078

d. 0.165

e. 0.140

Answer: C

24. A study conducted at a certain university shows that 55 % of the university՚s graduates obtain a job in their chosen field within one year after graduation. 15 graduates are selected at the university at random one year after graduation. What is the probability that exactly 7 of them will have found a job in their chosen field?

a. 0.201

b. 0.051

c. 0.078

d. 0.165

e. 0.140

Answer: D

25. A study conducted at a certain university shows that 55 % of the university՚s graduates obtain a job in their chosen field within one year after graduation. 15 graduates are selected at the university at random one year after graduation. What is the probability that exactly 10 of them will have found a job in their chosen field?

a. 0.201

b. 0.051

c. 0.078

d. 0.165

e. 0.140

Answer: E

26. It is believed that 70 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that exactly 7 of the 10 students got A՚s for matric?

a. 0.267

b. 0.233

c. 0.121

d. 0.250

e. 0.282

Answer: A

27. It is believed that 70 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that exactly 8 of the 10 students got A՚s for matric?

a. 0.267

b. 0.233

c. 0.121

d. 0.250

e. 0.282

Answer: B

28. It is believed that 70 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that exactly 9 of the 10 students got A՚s for matric?

a. 0.267

b. 0.233

c. 0.121

d. 0.250

e. 0.282

Answer: C

29. It is believed that 75 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that exactly 7 of the 10 students got A՚s for matric?

a. 0.267

b. 0.233

c. 0.121

d. 0.250

e. 0.282

Answer: D

30. It is believed that 75 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that exactly 8 of the 10 students got A՚s for matric?

a. 0.267

b. 0.233

c. 0.121

d. 0.250

e. 0.282

Answer: E

31. A manufacturing company has produced a new car seat for infants and it is undergoing rigorous safety testing. The product will only be approved for usage if at least 14 out of a sample of 15 seats meet the safety requirements. What is the probability that the new product will be approved if each individual seat is three times as likely to meet the safety requirements as not?

a. 0.976

b. 0.997

c. 0.080

d. 0.003

e. 0.091

Answer: C

32. A recent survey in Cape Town revealed that 60 % of the vehicles traveling on highways, where speed limits are posted at 80 km per hour, were exceeding the limit. Suppose you randomly record the speeds of 10 vehicles traveling on the N1 where the speed limit is 80 km per hour. What is the probability that exactly ten vehicles are exceeding the limit?

a. 0.01

b. 0.006

c. 1

d. 0.00

e. 0.99

Answer: B

33. To harvest all the wheat from a field requires 5 sunny days (not necessarily consecutive) . The farmer has only one week (7 days) left to harvest his crop. Given that the probability of a sunny day is 0.8, what is the probability that the farmer will be able to get the crop harvested on time?

a. 0.725

b. 0.344

c. 0.176

d. 0.599

e. 0.275

Answer: E

34. A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river. Past trips and experience of the sponsor leads her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn. At the present time, there are five canoes approaching this treacherous section. Assume that the sponsor՚s estimate of the probability of a canoe overturning in this section of water is accurate. What is the probability that four of the five canoes will overturn?

a. 0.346

b. 0.156

c. 0.477

d. 0.985

e. 0.224

Answer: B

35. It is known that three out of every ten financial institutions prefer debt-financing to equity-financing. A random sample of twenty financial institutions was selected. What is the probability that exactly 13 of the twenty companies sampled preferred preferred equity-financing to debt-financing?

a. 0.885

b. 0.995

c. 0.003

d. 0.164

e. 0.228

Answer: D

36. Cape Town is estimated to have 21 % of homes whose owners subscribe to the satellite television service, DSTV. If a random sample of four homes is taken, what is the probability that all four homes subscribe to DSTV?

a. 0.2100

b. 0.5000

c. 0.8791

d. 0.0021

e. 0.0019

Answer: E

37. A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river. Past trips and experience of the sponsor leads her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn. At the present time, there are five canoes approaching this treacherous section. Assume that the sponsor՚s estimate of the probability of a canoe overturning in this section of water is accurate. What is the probability that less than two of the five canoes will overturn?

a. 0.187

b. 0.031

c. 0.246

d. 0.317

e. 0.500

Answer: A

38. It is believed that 70 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that at most 7 of the 10 students got A՚s for matric?

a. 0.617

b. 0.851

c. 0.972

d. 0.474

e. 0.756

Answer: A

39. It is believed that 70 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that at most 8 of the 10 students got A՚s for matric?

a. 0.617

b. 0.851

c. 0.972

d. 0.474

e. 0.756

Answer: B

40. It is believed that 70 % of STA1000S students got A՚s for their final matric exams. Ten students are randomly chosen. What is the probability that at most 9 of the 10 students got A՚s for matric?

a. 0.617

b. 0.851

c. 0.972

d. 0.474

e. 0.756

Answer: C