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.
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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
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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
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