Workshop 6_Solutions(1)

Workshop 6_Solutions(1) - BUSS1020 Quantitative Business...

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BUSS1020 Quantitative Business Analysis University of Sydney Workshop 6 Solutions Prepared by: Scott Liu Workshop Aims 1) Use normal tables, Excel and StatCrunch to calculate a normal probability. 2) Use normal tables, Excel and StatCrunch to calculate a specific value given the normal probability. 3) Translate problems into a probability statement and solve them. 4) Perform calculations involving the Uniform distribution. 5) Perform calculations for the exponential distribution.
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BUSS1020 Quantitative Business Analysis Workshop 6 Solutions Workshop 6 Question 1 (BLS Q1, p. 246) Given a standardised normal distribution (with mean of 0 and a standard deviation of 1), what is the probability that: (a) Z is less that 1.57? (b) Z is greater than 1.84? (c) Z is between 1.57 and 1.84? (d) Z is less than 1.57 or greater than 1.84? Solution (a) Z is less that 1.57? P ( Z < 1.57) = 0.9418 (b) Z is greater than 1.84? P ( Z > 1.84) = 1 - P ( Z < 1.84) = 1 - 0.9671 = 0.0329 (c) Z is between 1.57 and 1.84? P (1.57 < Z < 1.84) = P ( Z < 1.84) - P ( Z < 1.57) = 0.9671 - 0.9418 = 0.0253 (d) Z is less than 1.57 or greater than 1.84? P ( Z > 1.57 or Z > 1.84) = P ( Z < 1.57) + P ( Z > 1.84) = 0.9418 + 0.0329 = 0.9747 University of Sydney Page 2
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BUSS1020 Quantitative Business Analysis Workshop 6 Solutions Question 2 (BLS Q6, p. 246) Given a normal distribution with μ = 50 and σ = 4, what is the probability that: (a) X > 43?
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