final_2004

# final_2004 - Student Name Student Number Faculty of Science...

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Student Name: Student Number: Faculty of Science FINAL EXAMINATION Mathematics 203 Principles of Statistics I Monday, December 20th 9a .m .-12Noon Answer directly on the test (use front and back if necessary). Calculators are allowed. One 8.5” × 11” two-sided sheet of notes is allowed. Language dictionaries are allowed. There are 15 pages to this exam and 3 pages of tables. The total number of marks for the exam is 100. Examiner: Professor Russell Steele Associate Examiner: Professor Masoud Asgharian 1

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Question 1: (10 points) A large airline keeps track of the number of no-shows for one of its most important commuter Fights. Over time the airline has found that the number of ticketed passengers who do not show up is a random variable with this probability distribution: X = x 0 1 2 3 4 5 6 7 8 Pr( X = x ) 0.05 0.08 0.13 0.23 0.18 0.13 0.08 0.06 0.06 (a) What is the probability that at most six passengers DO NOT show up for the Fight? (5 points) Pr( X 6) = 1 - Pr( X 7) = 1 - (0 . 06 + 0 . 06) = 0 . 88 (b) If the Fight holds 35 people and the airline routinely overbooks the Fight by selling 39 tickets, what is the probability that on any given day every passenger who shows up will get a seat? (5 points) Pr(no one has to miss the Fight) = Pr( X 4) = 1 - (0 . 05 + 0 . 08 + 0 . 13 + 0 . 23) = 0 . 51 2
Question 2: (6 points) The amount of money earned per month by a nurse practitioner is a normally distributed random variable with mean \$5000 and standard deviation \$1200. (a) What percentage of nurse practitioners earn more than \$4000 per month? (2 points) Pr( Y 4000) = Pr( Z 4000 - 5000 1200 ) =P r ( Z ≥- 0 . 83) =0 . 7967 (b) What percentage of nurse practitioners earn less than \$3000 per month? (2 points) Pr( Y 3000) = Pr( Z 3000 - 5000 1200 ) r ( Z ≤- 1 . 67) . 0475 (c) What is the probability that a randomly selected nurse practitioner earns between \$3250 and \$3800 per month? (2 points) Pr(3250 Y 3800) = Pr( 3250 - 5000 1200 Z 3800 - 5000 1200 ) r ( - 1 . 46 Z 1) . 1587 - 0 . 0721 = 0 . 0865 3

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Question 3: (12 points) In an attempt to determine whether two well-knownma i l -ordercom - panies had similar pricing strategies, a marketing frm askedbothcompan iesForthe irpr iceson each oF 10 pieces oF soFtware that both companies sold. The data are: SoFtware Package Computability PC Connection A 29 32 B 95 90 C 59 60 D 29 24 E 200 200 ± 58 48 G 120 120 H 180 179 I 220 230 J 38 33 Decimal point is 2 digits to the right of the line Computability magazine 0|3 3 4 0|6 6 1|0 2 1|8 2|0 2 Mean: 102.8 Stdev: 73.4 PC Connection 0|2 3 3 0|5 6 9 1|2 3 Mean: 101.6 Stdev: 76.6 4
(a) Test for a diFerence in prices at the companies at a signi±cance level of α =0 . 10 using only the sample means and standard deviations given above .(6po in t s ) H 0 : μ A - μ B H A : μ A - μ B ± s 2 p = 9 * 76 . 6 2 +9 * 73 . 6 2 18 =5627 . 56 Z = 102 . 8 - 101 . 6 ± 5267 . 56 / 10 + 5267 . 56 / 10 . 04 t 18 , 0 . 05 =1 . 73 and | 0 . 04 | < 1 . 73 so we cannot reject the null hypothesis that there is no diFerence between the two companies.

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final_2004 - Student Name Student Number Faculty of Science...

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