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:
The probability that a person chooses a car for the safety reason is 7/25 or 0.28 or 28%
The probability that a person chooses a car for the reliability reason is 31/300 or 0.10 or
10%
The probability that a person chooses a car for the cost reason is 23/150 or 0.15 or 15%
The probability that a person chooses a car for the performance reason is17/150 or 0.11
or 11%
The probability that a person chooses a car for the comfort reason is 47/300 or 0.16 or
16%
The probability that a person chooses a car for the looks reason is 9/100 or 0.09 or 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.
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.
Solution:
a) Find the probability of picking a lens that is scratched or flaked.
The probability of picking a lens that is scratched or flaked is (5865/25891) +
(1992/25891) - (5865/25891) * (1992/25891) = 0.321
b) Find the probability of picking a lens that is the wrong PD or was lost in lab.
The probability of picking a lens that is wrong PD or was lost in lab is (1398/25891)
+ (976/25891)- (1398/25891) * (976/25891) = 0.094
c) Find the probability of picking a lens that is not scratched.
The probability of picking a lens that is not scratched
1-(5865/25891) =0.773
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