STAT 200 Week 3 Homework Problems[Solved] A+ Guide

STAT 200 Week 3 Homework Problems 4.1.4 A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person c hooses a given car, and that data is in table #4.1.4 ("Car preferences," 2013). Table #4.1.4: Reason for Choosing a Car Safety Reliability Cost Performance Comfort Looks 27 Find the probability a person chooses a car for each of the given reasons. Solution:  The probability that a person chooses a car for the safety reason is 7/25 or 0.28 or 28%  The probability that a person chooses a car for the reliability reason is 31/300 or 0.10 or 10%  The probability that a person chooses a car for the cost reason is 23/150 or 0.15 or 15%  The probability that a person chooses a car for the performance reason is17/150 or 0.11 or 11%  The probability that a person chooses a car for the comfort reason is 47/300 or 0.16 or 16%  The probability that a person chooses a car for the looks reason is 9/100 or 0.09 or 9% 4.2.2 Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a time period. Table #4.2.2 gives the defect and the number of defects. Table #4.2.2: Number of Defective Lenses Defect type Number of defects Scratch 5865 Right shaped – small 4613 Flaked 1992 Wrong axis 1838 Chamfer wrong 1596 Crazing, cracks 1546 Wrong shape 1485 Wrong PD 1398 Spots and bubbles 1371 Wrong height 1130 Right shape – big 1105 Lost in lab 976 Spots/bubble – intern 976 a.) Find the probability of picking a lens that is scratched or flaked. b.) Find the probability of picking a lens that is the wrong PD or was lost in lab. c.) Find the probability of picking a lens that is not scratched. d.) Find the probability of picking a lens that is not the wrong shape. Solution: a) Find the probability of picking a lens that is scratched or flaked. The probability of picking a lens that is scratched or flaked is (5865/25891) + (1992/25891) - (5865/25891) * (1992/25891) = 0.321 b) Find the probability of picking a lens that is the wrong PD or was lost in lab. The probability of picking a lens that is wrong PD or was lost in lab is (1398/25891) + (976/25891)- (1398/25891) * (976/25891) = 0.094 c) Find the probability of picking a lens that is not scratched. The probability of picking a lens that is not scratched 1-(5865/25891) =0.773