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.
Answer: Total reasons for choosing a car = 84+62+46+34+47+27 =300
Safety Probability 84/300= 0.28
Reliability Probability 62/300= 0.21
Cost Probability 46/300= 0.15
Performance Probability 34/300= 0.11
Comfort Probability 47/300= 0.16
Looks Probability 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
Answer: Sum of total Defects =25891
a.) Find the probability of picking a lens that is scratched or flaked. 5865+ 1992/25891
= .304
b.) Find the probability of picking a lens that is the wrong PD or was lost in lab.
1398+976/25891 = .092
c.) Find the probability of picking a lens that is not scratched. 1-5865/25891 = 0.773
d.) Find the probability of picking a lens that is not the wrong shape. 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.
Possible # of outcomes are 38, n=38
a.) Find the probability of winning if you pick the number 7 and it comes up on the
wheel.
Probability 1/38 = 0.02632
b.) Find the odds against winning if you pick the number 7.
Odds against = P (Event will not happen)/ P (Event will happen)
1-0.02632/ 0.02632 = .97368/.02632 =36.99 then Odds against winning if you pick 7 =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 slots on the wheel if you pay $1.oo for each slot then you pay $38. If you win
then the casino will pay you $20.00 .
Casino Profit = $38 - $20 = $18.00
4.4.6 Find
10P6
n = 10 r = 6
10! / (10-6)! = 151200
4.4.12 How many ways can you choose seven people from a group of twenty?
n = 20 r =7
20! / 7! (20-7)! = 20! / 7!13! = 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.
Random variable X = number of heads
Let, H= Heads, T = Tails
b) Write the probability distribution for the number of heads.
Combinations are
TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
Number of
Heads(X) 0 1 2 3
Probability(P) 1/8 3/8 3/8 1/8
c) Draw a histogram for the number of heads.
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