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COMSATS Institute of Information Technology Islamabad MTH 161 Introduction to Statistics Solution of Quiz 5 Program: BBA Date: Dec 19, 2012 Total Points: 10 Instructor: Shahzad Fazal Bhatti Solution for Left The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time a. more than 19.5 hours? Let X = time taken to assemble a randomly selected car, then X is a normal random variable with mean 20 hours and a standard deviation of 2 hours. Suppose x1 = 19.5, then x1 − 20 19.5 − 20 z1 = = = −0.25 2 2 P (X > 19.5) = 1 − P (X < 19.5) = 1 − P (Z < −0.25) = 1 − 0.4013 = 0.5987 b. between 20 and 22 hours? Suppose x2 = 20 and x3 = 22, then z2 = x1 − 20 20 − 20 = = 0.00 2 2 z3 = 22 − 20 x1 − 20 = = 1.00 2 2 P (20 < X < 22) = P (X < 22) − P (X < 20) = P (Z < 1.00) − P (Z < 0.00) = 0.8413 − 0.50 = 0.3413 Solution for Right The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last a. less than 7 months. Let Y = life span of a randomly selected instrument produced by the machine, then Y is a normal random variable with mean 12 months and a standard deviation of 2 months. Suppose y1 = 7, then y1 − 12 7 − 12 z1 = = = −2.5 2 2 P (Y < 7) = P (Z < −2.5) = 0.0062 b. between 7 and 12 months. suppose that y2 = 12, then z2 = y2 − 12 12 − 12 = = 0.00 2 2 P (7 < X < 12) = P (X < 12) − P (X < 7) = P (Z < 0.00) − P (Z < −2.5) = 0.50 − 0.0062 = 0.4938 Points Distribution: Part (a) Part (b) Total 4 6 10