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. Total frequency = 84+62+46+34+47+27 = 300 The probability a person chooses a car for safety = 84/300 = 0.280 The probability a person chooses a car for reliability = 62/300 = 0.207 The probability a person chooses a car for cost = 46/300 = 0.153 The probability a person chooses a car for performance = 34/300 = 0.113 The probability a person chooses a car for comfort = 47/300 = 0.157 The probability a person chooses a car for looks = 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 5865+4613+1992+1838+1596+1546+1485+1398+1371+1130+1105+976+976 = 25891 a.) Find the probability of picking a lens that is scratched or flaked. P(AUB) = P (A) + P (B) – P(A∩B) = (5865+1992) / (25891) - 25891 x 1992/25891 = 0.321 b.) Find the probability of picking a lens that is the wrong PD or was lost in lab. P(AUB) = P(A) + P(B) – P A∩B) (1398+976) / /25891 x 976/25891 = 0.094 c.) Find the probability of picking a lens that is not scratched. P(A) = 1 – P(A) = 1 – 5865/25891 = 0.773 d.) Find the probability of picking a lens that is not the wrong shape. P(A) = 1 – P(A) 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. The possible number of outcomes are 38 a.) Find the probability of winning if you pick the number 7 and it comes up on the wheel. Probability = 7/38 = 0.02632 b.) Find the odds against winning if you pick the number 7. Odds against winning = P (event will not happen) / P (event will happen) = 1-0.02632/0.02632 = 36.99 ≅ 37 If you pick number 7, then odds against winning is 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 spots on the wheel and need $1 to bet and the casino owner gets $38 in one game from which he gives $20 for winning person whose number comes up. Profit casino making on the bet = 38-20 = $18