STAT 200 Week 3 Homework Problems.

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 chooses 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 84 62 46 34 47 27 Find the probability a person chooses a car for each of the given reasons. Solution: Safety: 84/300 = 28% Reliability: 62/300 = 21% Cost: 46/300 = 15% Performance: 34/300 = 11% Comfort: 47/300 = 15% Looks: 27/300 = 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. This study source was downloaded by 100000831157179 from CourseHero.com on 09-13-2021 08:25:46 GMT -05:00 https://www.coursehero.com/file/34763431/Farrell-Week-3-HWdocx/ This study resource was shared via CourseHero.com 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. a) Scratched: 5865/25891 = 22% Flaked: 1992/25891 = 7% b) Wrong PD: 1398/25891 = 5% Lost in lab: 976/25891 = 37% c) Not scratched: Right shaped (big) + Right shaped (small)/25891 5708/25891 = 22% d) Wrong shape: 1485/25891 = 5% 4.2.8 In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. a.) Find the probability of winning if you pick the number 7 and it comes up on the wheel. Probability: 1/38 b.) Find the odds against winning if you pick the number 7. Solution: 1-1/38 37/38 c.) The casino will pay you $20 for every dollar you bet if your number comes up. How much profit is the casino making on the bet? The Expected gain is 1/38 *20 = $0.58 37/38 - 19*1/38 = = 0.474 Profit casino is making on the bet = $0.474 4.4.6 Find 10P6 Npr = n!/(n-r)! 10p6 = 10!/(10-6)! Numerator n!: N! = 10! 10! = 10*9*8*7*6*5*4*3*2*1 10! = 3,628,800 Denominator: (n-r)! = (10-6)! (10-6)! = 4! 4!=4*3*2*1