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

SafetyReliabilityCostPerformanceComfortLooks
846246344727

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 typeNumber of defects
Scratch5865
Right shaped – small4613
Flaked1992
Wrong axis1838
Chamfer wrong1596
Crazing, cracks1546
Wrong shape1485
Wrong PD1398
Spots and bubbles1371
Wrong height1130
Right shape – big1105
Lost in lab976
Spots/bubble – intern976
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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