# Stat 200 week 3 homework solutions

**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.