STAT 200 Week 3 Homework Problems 100% PASS

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 chooses a given car, ...

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 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 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 4!=24 Premutation value: 10p6 = 3,628,800/24 Solution: 10p6 = 151,200 4.4.12 How many ways can you choose seven people from a group of twenty? N = 20, r = 7 20c7 = 20!/7!(20-7) = 20!/7!13! = 77520 Solution: 77520 5.1.2 Suppose you have an experiment where you flip a coin three times. You then count the number of heads. a.) State the random variable. Coin b.) Write the probability distribution for the number of heads. Binomial distribution = p(x=r)=Cn/p^r q^n-r Cn/r= n!/r!n-r! c.) Draw a histogram for the number of heads. d.) Find the mean number of heads. e.) Find the variance for the number of heads. f.) Find the standard deviation for the number of heads. g.) Find the probability of having two or more number of heads. h.) Is it unusual to flip two heads? 5.1.4 An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years? Expected value = $70.32 1 – 0.2 = 0.8 2 year extended warrantee 112.10 Dishwasher 800 800*0.2 = 160 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