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.
Safety: 84/300= 28%
Reliability: 62/300= 21%
Cost: 46/300= 15%
Performance: 34/300= 11%
Comfort: 47/300= 16%
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
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a.) Find the probability of picking a lens that is scratched or flaked.
A: 7,857/25,891
b.) Find the probability of picking a lens that is the wrong PD or was lost in lab.
A: 2,374/25,891
c.) Find the probability of picking a lens that is not scratched.
A: 20,026/25,891
d.) Find the probability of picking a lens that is not the wrong shape.
A: 24,406/25,891
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.
1/38 chance
b.) Find the odds against winning if you pick the number 7.
37/1 odds against winning
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?
A: If you win, you gain of $19. If you lose, you lose 1$
expected value = 19(1/38) + (-1)(37/38) = -0.4736
The casino is making 47 cents profit on your $1 bet
4.4.6 Find 10P6
A:
10! / (10-6)!
10! / 4!
151,200
4.4.12 How many ways can you choose seven people from a group of twenty?
C (n,r)= (n! / (r! (n-r)! ) C (20, 7) = (20! / (7! (20-7)! )= 77,520
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