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.
Total = 84+62+46+34+47+27=300
P(Safety) = 84/300=0.28
P(Reliability) = 62/300=0.27
P(Cost) = 46/300=0.15
P(Performance) = 34/300=0.11
P(Comfort) = 47/300=0.16
P(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
, a.) Find the probability of picking a lens that is scratched or flaked.
Scratch + Flaked = 5865+1992=7857
7857/25891=0.303
b.) Find the probability of picking a lens that is the wrong PD or was lost in lab.
Wrong PD + Lost in lab = 1398+976=2374
2374/25891=0.091
c.) Find the probability of picking a lens that is not scratched.
P(Scratch) = 5865/25891=0.227
P(Not scratch) = 1-0.227=0.773
d.) Find the probability of picking a lens that is not the wrong shape.
P(Wrong shape) = 1485/25891=0.057
P(Not wrong shape) = 1-0.057=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.
a.) Find the probability of winning if you pick the number 7 and it comes up on the
wheel.
P(7)= 1/38=0.026
b.) Find the odds against winning if you pick the number 7.
P(Not 7)= 37/38=0.974
Odds against 7 = P(Not 7)/P(7) = 37//38 = 37:1
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 actual odds is 37:1, meaning the casino would pay $37 on every $1 bet. The
casino actually pays $20 for every $1 bet. Therefore, the profit is $37-$20=$17
4.4.6 Find = 10!/(10-6)! = 10!/4! = 151200
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!x13!) = 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.
x=number of heads.
b.) Write the probability distribution for the number of heads.
7 successful trials out of 8 total.
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.
Total = 84+62+46+34+47+27=300
P(Safety) = 84/300=0.28
P(Reliability) = 62/300=0.27
P(Cost) = 46/300=0.15
P(Performance) = 34/300=0.11
P(Comfort) = 47/300=0.16
P(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
, a.) Find the probability of picking a lens that is scratched or flaked.
Scratch + Flaked = 5865+1992=7857
7857/25891=0.303
b.) Find the probability of picking a lens that is the wrong PD or was lost in lab.
Wrong PD + Lost in lab = 1398+976=2374
2374/25891=0.091
c.) Find the probability of picking a lens that is not scratched.
P(Scratch) = 5865/25891=0.227
P(Not scratch) = 1-0.227=0.773
d.) Find the probability of picking a lens that is not the wrong shape.
P(Wrong shape) = 1485/25891=0.057
P(Not wrong shape) = 1-0.057=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.
a.) Find the probability of winning if you pick the number 7 and it comes up on the
wheel.
P(7)= 1/38=0.026
b.) Find the odds against winning if you pick the number 7.
P(Not 7)= 37/38=0.974
Odds against 7 = P(Not 7)/P(7) = 37//38 = 37:1
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 actual odds is 37:1, meaning the casino would pay $37 on every $1 bet. The
casino actually pays $20 for every $1 bet. Therefore, the profit is $37-$20=$17
4.4.6 Find = 10!/(10-6)! = 10!/4! = 151200
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!x13!) = 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.
x=number of heads.
b.) Write the probability distribution for the number of heads.
7 successful trials out of 8 total.
