# 5 of 7 opmt 1130 review exercises 28 an exam has 6

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Chapter Apx / Exercise 12
Essentials of Statistics for the Behavioral Sciences
Gravetter/Wallnau
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Chapter Apx / Exercise 12
Essentials of Statistics for the Behavioral Sciences
Gravetter/Wallnau
Expert Verified
OPMT 1130 Review exercises  28. An exam has 6-multiple choice questions with each question having 4 possible answers.  The student did not studyand randomly selects answers.   (a)It takes at least 3 correct to pass the test.  What is the probability the student passes? (b)What is the probability the student gets the first three questions in a row correct? (c)A different exam has 48-multiple choice questions with each question having 4 possible answers.  The student did not study and randomly selects answers.  Find the probability thestudent gets:i)at least 20 questions correct.   (ii) at most 14 questions correct    (iii) from 11-14 correct29. Royal Cruises offers 4-day cruises between Victoria and Seattle. Typically 400 passengers make reservations on the cruise. Historical records indicate that 10% of passengers cancel their reservation, due to illness or injury, just before the departure date. If fewer than 350 passengers go on the cruise Royal Cruises will not recover their fixed costs of \$125,000. Whatis the probability they will be able to recover their fixed costs on their next cruise?30. 80% of the illegally parked cars in Surrey get tickets. In a sample of 100 illegally parked cars what is the probability that more than 75 of the cars received tickets?
6.(a) TSX: 10% Bond Fund: 25% (b) The Bond fund is riskier because the coefficient of variation is much larger. As a percentage of the mean the price fluctuates much more. 7. 0.1057 8.0.7648 9.(a) 0.2241 (b) 0.0650 10. (a) 0.54 (b) see below (c) 0.10 (d) 0.4194 BBTotalS.26.28.54S.36.10.46Total.62.381.00(e) P(Stocks and Bonds) =? P(Stocks) × P(Bonds) Could use the letters S and Binstead0.26 0.54×0.62 so No, they are NOT independent events.ALT: Use the answer to part (a) and (d) P(stock | bonds) = 0.4194 P(stocks) = 0.5400 Less likely to buy stocks if you already bought bonds so the events are NOT independent.11.(a) 105/252 = 0.4167 (b) (21 +105 + 105)/252 = 0.9167 OR 1 - P(5) = 1-21/252 = 0.916712.(a) 0.6916 (b) 0.0836 13. 3% 14. 1- 462/3003= 0.8462 15.(a) 0.1606, µ = 6 (b) 0.4232, µ = 316.(a) 0.8507 (b) 0.0308 17. 56/120 = 0.4667 18.(a) 0.3000 (b) 40.00% (c) 0.7200 (d) 0.2800 (e) 0.3000 (f) 0.4000 (g) see next page6 of 7
OPMT 1130 Review exercises  (g) Method 1:P(Woman and In Default) =? P(Woman) × P(In Default) 24/200 = ? 80/200 × 60/200 0.12 = 0.12 → independent of genderMethod 2:P(In Default) = 60/200 P(In Default | Woman) = 24/80 = 0.30P(In Default) = P(In Default |Woman) → independent of genderOverall 30% of students are in default on their loan. 30% of women (and 30% of men) are in default so whether or not a student defaults on their loan does notdepend on their gender. 19. (a) 0.1500 (b) 0.5000 (c) 0.3750 ( d) 60.00% (e) 0.8333 (f) No, can be male andmarried at the same timeMaleFemale TotalMarried50100150Single302050Total80120200(g) Method 1:P(male and married) = ? P(male) × P(Married) 50/200 = ? 80/200 × 150/200 0.25 ≠ 0.30 → No, marital status depends on gender.Method 2:P(Married) = 150/200 = 0.75 P(Married | Male) = 50/80=0.6250.625 ≠ 0.75