Stat 200 week 3 homework solutions

Stat 200 week 3 homework solutions

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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.
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.
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 10P6
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>=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.

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