STAT 260 Final: STAT 260 Final Exam 1
31 Jan 2019
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Supplement for Statistics 260 Sample Final Examination 1 4 - 1
STATISTICS 260
SAMPLE FINAL EXAMINATION 1
(from Spring Term 2001)
INSTRUCTIONS:
1. Use a PENCIL HB or softer.
2. Your NAME and STUDENT NUMBER must be recorded on BOTH your question paper and in
CODED FORM on your green answer sheet.
3. Hand calculators are permitted; calculator memories must be cleared just before the examination
begins. No other aids are permitted, except the Formula List and Statistical Tables which are
provided.
4. Questions 1 through 32 are multiple-choice questions worth 2 marks each. Code your answers
on the green answer sheet provided. For questions requiring numerical answers, the 10 choices are
listed in numerically increasing order. Choose the value that is nearest your (unrounded) answer.
In the special case that your (unrounded) answer is equidistant from the two nearest choices, choose the
larger of these two choices. For verification purposes, show all calculations on your question
paper. Unverified answers may be disallowed.
5. Questions 33 and 34 are full-answer questions worth 8 marks each. For each of these questions
write out your solution carefully and completely on the question paper. Marks will be deducted for
incomplete or poorly presented solutions.
Maximum Score is 80 marks.
Note: To conserve paper, no working space is provided on this sample exam. Working space will be
provided on the real exam.
Questions 1 through 3 refer to the following setup. CM Company manufactures computer monitors
at three different sites: Plant A, Plant B, Plant C. Monitors not requiring any warranty service are given
a High Quality rating at the end of the warranty period, monitors requiring warranty service are given a
Medium Quality rating, and monitors requiring replacement under warranty are given a Low Quality
rating. The following table gives proportions of CM’s total production for the various categories.
Quality Rating
High Medium Low
Plant A.13 .24 .03
Plant B.09 .21 .05
Plant C.08 .15 .02
Suppose a CM Monitor is purchased (at random from CM’s inventory).
Supplement for Statistics 260 Sample Final Examination 1 4 - 2
1. What is the probability that the purchased monitor was manufactured by Plant C or will receive a
High Quality rating?
(A) .45 (B) .50 (C) .55 (D) .60 (E) .65
(F) .70 (G) .75 (H) .80 (I) .85 (J) .90
2. If the purchased monitor was manufactured by Plant A, what is the probability that it will earn a Low
Quality rating?
(A) .02 (B) .04 (C) .06 (D) .08 (E) .10
(F) .12 (G) .14 (H) .16 (I) .18 (J) .20
3. Which of the following statements are true?
(i) The events “purchased monitor was manufactured by Plant A” and “purchased monitor was
manufactured by Plant B” are independent.
(ii) The events “purchased monitor was manufactured by Plant A” and “purchased monitor was
manufactured by Plant B” are mutually exclusive.
(iii) The events “purchased monitor will receive a High Quality rating” and “purchased monitor was
manufactured by Plant C” are independent.
(A) None (B) Only (i) (C) Only (ii) (D) Only (iii)
(E) (i) & (ii) (F) (i) & (iii) (G) (ii) & (iii) (H) All
Questions 4 through 6 refer to the following setup. A manufacturer of a certain model of car has
recalled all sold units to correct a brake defect. A second recall was necessary when a second brake
defect was discovered. 55% of the owners of the affected cars responded to both recalls; 30% responded
only to the first recall; 15% percent responded to neither recall. The probability that a malfunction in the
brakes occurs during the warranty period after the second recall notice was issued is:
.1 for cars whose owners responded to both recalls,
.3 for cars whose owners responded only to the first recall,
.8 for cars whose owners responded to neither recall.
4. What is the probability that a car randomly chosen from all those sold, experiences a brake
malfunction during the warranty period after the second recall?
(A) .05 (B) .10 (C) .15 (D) .20 (E) .25
(F) .30 (G) .35 (H) .40 (I) .45 (J) .50
5. If a car randomly chosen from all those sold experiences a brake malfunction during the warranty
period after the second recall, what is the probability that the owner responded to neither recall?
(A) .40 (B) .45 (C) .50 (D) .55 (E) .60
(F) .65 (G) .70 (H) .75 (I) .80 (J) .85
6. For a randomly chosen owner, what is the expected value of the number X of recall notices the car
owner responded to?
(A) 1.00 (B) 1.05 (C) 1.10 (D) 1.15 (E) 1.20
(F) 1.25 (G) 1.30 (H) 1.35 (I) 1.40 (J) 1.45
Supplement for Statistics 260 Sample Final Examination 1 4 - 3
Questions 7 through 9 refer to the following setup. The route used by a certain motorist in
commuting to work passes through three traffic lights. The probability that the commuter must stop at
the first, second, third traffic light is .4, .5, .7, respectively. Assume the three events: “commuter must
stop at the first traffic light”, “commuter must stop at the second traffic light”, “commuter must stop at
the third traffic light”, are independent events.
7. What is the probability that on the way to work the commuter must stop all three traffic lights?
(A) .01 (B) .04 (C) .07 (D) .10 (E) .13
(F) .16 (G) .19 (H) .22 (I) .25 (J) .28
8. What is the probability that on the way to work the commuter must stop at exactly one of the three
traffic lights?
(A) .05 (B) .10 (C) .15 (D) .20 (E) .25
(F) .30 (G) .35 (H) .40 (I) .45 (J) .50
9. What is the probability that the commuter will not have to stop at any of the three lights on exactly
one of the next five trips to work? (i.e. What is the probability that exactly one of the next five trips to
work will be stop-free?)
(A) .05 (B) .10 (C) .15 (D) .20 (E) .25
(F) .30 (G) .35 (H) .40 (I) .45 (J) .50
Questions 10 and 11 refer to the following setup. Suppose that trees are randomly distributed over a
certain forest region at the average rate of 60 trees per hectare.
10. What is the probability that in a certain one-quarter hectare plot there will be at most 10 trees?
(A) .05 (B) .10 (C) .15 (D) .20 (E) .25
(F) .30 (G) .35 (H) .40 (I) .45 (J) .50
11. Given that there are at most 20 trees in a certain one-quarter hectare plot, what is the probability that
there are more than 10 trees in this plot?
(A) .66 (B) .69 (C) .72 (D) .75 (E) .78
(F) .81 (G) .84 (H) .87 (I) .90 (J) .93
12. Assume that 60% of all households in a certain large city have microwave ovens. What is the
probability that 20 households chosen at random from this city will include at least 13 households
having microwave ovens?
(A) .25 (B) .30 (C) .35 (D) .40 (E) .45
(F) .50 (G) .55 (H) .60 (I) .65 (J) .70
Questions 13 through 15 refer to the following setup. The reaction time (in tenths of seconds) to a
certain stimulus is a continuous random variable with pdf: .
Document Summary
Sample final examination 1 (from spring term 2001) Instructions: use a pencil hb or softer, your name and student number must be recorded on both your question paper and in. Coded form on your green answer sheet: hand calculators are permitted; calculator memories must be cleared just before the examination begins. No other aids are permitted, except the formula list and statistical tables which are provided: questions 1 through 32 are multiple-choice questions worth 2 marks each. Code your answers on the green answer sheet provided. For questions requiring numerical answers, the 10 choices are listed in numerically increasing order. Choose the value that is nearest your (unrounded) answer. In the special case that your (unrounded) answer is equidistant from the two nearest choices, choose the larger of these two choices. For verification purposes, show all calculations on your question paper. Unverified answers may be disallowed: questions 33 and 34 are full-answer questions worth 8 marks each.
