Statistics > STUDY GUIDE > STAT 200 Week 3 Homework Problems 1 (All)

STAT 200 Week 3 Homework Problems 1

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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 84 62 46 34 47 27 Find the probability a person chooses a car for each of the given reasons. Answer: Total reasons for choosing a car = 84+62+46+34+47+27 =300 Safety Probability 84/300= 0.28 Reliability Probability 62/300= 0.21 Cost Probability 46/300= 0.15 Performance Probability 34/300= 0.11 Comfort Probability 47/300= 0.16 Looks Probability 27/300= 0 .09 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 Answer: Sum of total Defects =25891 a.) Find the probability of picking a lens that is scratched or flaked. 5865+ 1992/25891 = .304 b.) Find the probability of picking a lens that is the wrong PD or was lost in lab. 1398+976/25891 = .092 c.) Find the probability of picking a lens that is not scratched. 1-5865/25891 = 0.773 d.) Find the probability of picking a lens that is not the wrong shape. 1-1485/25891= 0.943 4.2.8 In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. Possible # of outcomes are 38, n=38 a.) Find the probability of winning if you pick the number 7 and it comes up on the wheel. Probability 1/38 = 0.02632 b.) Find the odds against winning if you pick the number 7. Odds against = P (Event will not happen)/ P (Event will happen) 1-0.02632/ 0.02632 = .97368/.02632 =36.99 then Odds against winning if you pick 7 =37 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? There are 38 slots on the wheel if you pay $1.oo for each slot then you pay $38. If you win then the casino will pay you $20.00 . Casino Profit = $38 - $20 = $18.00 4.4.6 Find 10P6 n = 10 r = 6 10! / (10-6)! = 151200 4.4.12 How many ways can you choose seven people from a group of twenty? n = 20 r =7 20! / 7! (20-7)! = 20! / 7!13! = 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. Random variable X = number of heads Let, H= Heads, T = Tails b) Write the probability distribution for the number of heads. Combinations are TTT, TTH, THT, THH, HTT, HTH, HHT, HHH Number of Heads(X) 0 1 2 3 Probability(P) 1/8 3/8 3/8 1/8 c) Draw a histogram for the number of heads. [Show More]

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