*label*Mathematics

### Question Description

**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 |

- 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

**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.)

b.)

c.)

d.)

e.)

f.)

**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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## Tutor Answer

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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

84

Reliability

62

Cost Performance

46

34

Comfort

47

Looks

27

Find the probability a person chooses a car for each of the given reasons.

Solution:

The total reasons for choosing a car is

=84+62+46+34+47+27

=300,

Total of reasons =300

Now we find the probability of reasons one by one

Probability of a person choosing a car for its safety feature is =84/300=0.28

Probability of a person choosing a car for its reliability is =62/300=0.206

Probability of a person choosing a car for its cost is =46/300=0.153

Probability of a person choosing a car for its performance is =34/300=0.113

Probability of a person choosing a car for its comfort =47/300=0.156

Probability of a person choosing a car for its look is =27/300=0.009

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 –

4613

small

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 –

976

intern

a.) Find the probability of...

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