UNIVERSITY OF BOTSWANA DEPARTMENT OF MATHEMATICS Question One MAT 271 TEST 1 Let a random variable W be given by WZ+Z+...+Zo where Z, are independent standard normal random variables for i = 1, 2, ..., 10. Find P(3.247W < 20.483) [7 marks] x-x Z = ก Question Two A boy flips a fair coin 100 independent times and a girl flips a fair coin 100 independent times. What is the probability that the boy will have 10 less tails than the girl? Question Three [7 marks] The random variable, X, representing the number of ice blocks in a drink, has the following probability distribution. H 4 5 6 7 f(x) = P(X = 1) 0.2 0.4 0.3 0.1 Find, using the normal approximation, the probability that in a sample of 36 drinks, the average number of ice blocks will be less than 5.5. [8 marks] P (W < 3.247) - P (W220.483) - 5.1 4-4-9 + -5 + - 5.2 253 1 p(x <5.5)=1 <)+(01)+5(04)+(0-3) + 7 (0.1) 1. (**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1) 29.9 1=36 ०=०.११

UNIVERSITY OF BOTSWANA DEPARTMENT OF MATHEMATICS Question One MAT 271 TEST 1 Let a random variable W be given by WZ+Z+...+Zo where Z, are independent standard normal random variables for i = 1, 2, ..., 10. Find P(3.247W < 20.483) [7 marks] x-x Z = ก Question Two A boy flips a fair coin 100 independent times and a girl flips a fair coin 100 independent times. What is the probability that the boy will have 10 less tails than the girl? Question Three [7 marks] The random variable, X, representing the number of ice blocks in a drink, has the following probability distribution. H 4 5 6 7 f(x) = P(X = 1) 0.2 0.4 0.3 0.1 Find, using the normal approximation, the probability that in a sample of 36 drinks, the average number of ice blocks will be less than 5.5. [8 marks] P (W < 3.247) - P (W220.483) - 5.1 4-4-9 + -5 + - 5.2 253 1 p(x <5.5)=1 <)+(01)+5(04)+(0-3) + 7 (0.1) 1. (**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1) 29.9 1=36 ०=०.११

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 6E

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