STAT 200 Week 3 Homework Problems4.1.4
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
84
Reliability
62
Cost
46
Performance
34
Comfort
47
Looks
27
Find the probability a person chooses a car for each of the given reasons.
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.)
b.)
c.)
d.)
Find the probability of picking a lens that is scratched or flaked.
Find the probability of picking a lens that is the wrong PD or was lost in lab.
Find the probability of picking a lens that is not scratched.
Find the probability of picking a lens that is not the wrong shape.
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.
b.) Find the odds against winning if you pick the number 7.
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?
4.4.6 Find
10
P6
4.4.12 How many ways can you choose seven people from a group of twenty?
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.
b.) Write the probability distribution for the number of heads.
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 warranty costs $112.10 on a dishwasher. What is the expected value of
the extended warranty assuming it is replaced in the first 2 years?
5.2.4
Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the
following probabilities using technology.
a.) P ( x = 1)
b.) P ( x = 5 )
c.) P ( x = 3)
d.) P ( x £ 3)
e.) P ( x ³ 5 )
f.) P ( x £ 4 )
5.2.10
The proportion of brown M&M’s in a milk chocolate packet is approximately 14% (Madison,
2013). Suppose a package of M&M’s typically contains 52 M&M’s.
a.) State the random variable.
b.) Argue that this is a binomial experiment
Find the probability that
c.) Six M&M’s are brown.
d.) Twenty-five M&M’s are brown.
e.) All of the M&M’s are brown.
f.) Would it be unusual for a package to have only brown M&M’s? If this were to
happen, what would you think is the reason?
5.3.4
Approximately 10% of all people are left-handed. Consider a grouping of fifteen people.
a.) State the random variable.
b.) Write the probability distribution.
c.) Draw a histogram.
d.) Describe the shape of the histogram.
e.) Find the mean.
f.) Find the variance.
g.) Find the standard deviation.
