# STAT 200 Week 3 Homework Problems (A+ Solutions)

STAT 200 Week 3 Homework Problems (A+ Solutions)
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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 Total: 25891

• 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.

• Find the probability of winning if you pick the number 7 and it comes up on the wheel.
• Find the odds against winning if you pick the number 7.
• 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 – 10P

• Numerator n!:
• Denominator:
• Premutation value:

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.

• State the random variable.
• Write the probability distribution for the number of heads.
• Draw a histogram for the number of heads.
• Find the mean number of heads.
• Find the variance for the number of heads.
• Find the standard deviation for the number of heads
• Find the probability of having two or more number of heads.
• 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.

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.

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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