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Stat 100A -Intro Probability. Old exam. J. Sanchez. UCLA Department of ... Cheat sheet can have only formulas and definitions, no solved problems, ...
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Old exam J. Sanchez UCLA Department of Statistics MUST DO BEFORE STARTING EXAM
(a) WRITE AND MARK YOUR NAME AND ID ON THE SCANTRON.
(b) WRITE THE COLOR OF THE EXAM ON THE TOP OF THE SCANTRON, IN NUMBER 2 PENCIL.
(c) WRITE YOUR NAME ON ALL SIDES OF THE CHEAT SHEET, TOP RIGHT HAND CORNER. MAKE SURE YOUR CHEAT SHEET IS STAPLED THROUGHOUT THE WHOLE EXAM.
(d) DO NOT DETACH ANY PAGES FROM THIS EXAM. EXAM MUST STAY STAPLED DURING THE WHOLE EXAM.
(e) PUT ALL YOUR BELONGINGS INSIDE YOUR BACKPACK UNDER THE CHAIR.
(f) ONLY ID, NUMBER 2 PENCIL AND PEN, ERASER, SCIENTIFIC CALCULATOR, SCANTRO- NAND CHEAT SHEET ALLOWED IN THE EXAM.
(g) PUT DOWN THE TABLES ON YOUR RIGHT AND LEFT. ALL ITEMS MUST BE ON YOUR DESK.
Other important Instructions–Read. Points lost for not following directions OR 0 POINTS IN THE EXAM, and further consequences.
Old exam J. Sanchez UCLA Department of Statistics
Old exam J. Sanchez UCLA Department of Statistics
(c) 0.
(d) 0.
(e) 0.
Solution 3. X = number of defectives in a sample of 3,
P(X > 1) =
2
1
3
3
0
3
Question 4. Rebuilt ignition systems leave an aircraft rework facility at a rate of three per hour, on average. The assembly line needs four ignition systems in the next hour. What is the probability that they will be available? (Note: making an appropriate assumption about the distribution of the random variable is part of this exercise).
(a) 0.
(b) 0.
(c) 0.
(d) 1
(e) 0.
Solution 4. Let Y= number of ignition systems that leave the facility at a given hour. Then Y can be assumed to be Poisson with parameter λ = 3.
P(Y ≥ 4) = 1 − P(Y ≤ 3) = 1 − 3
(^0) e− 3 0! −^
31 e−^3 1! − 3 (^2) e− 3 2! −^
33 e−^3 3! =^0.^3527681
Question 5. ApplewithWindows provides free examination of its products for seven days. If not completely sat- isfied, a customer can return the product within that period and get a full refund. According to past records of the company, an average of 2 of every 10 products sold by this company are returned for a refund. Using the Poisson probability distribution formula, find the probability that exactly 6 of the 40 products sold by this company on a given day will be returned for a refund.
(a) 0.
(b) 0.
(c) 0.
(d) 0.