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STAT 200 Week 3 Homework Problems 1) 4

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STAT 200 Week 3 Homework Problems

1) 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.

 

Total:

Safety:

Reliability:

Cost:

Performance:

Comfort:

Looks:

 

2) 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

 

1. Find the probability of picking a lens that is scratched or flaked.

 

2. Find the probability of picking a lens that is the wrong PD or was lost in lab.

 

3. Find the probability of picking a lens that is not scratched.

 

4. Find the probability of picking a lens that is not the wrong shape.

 

3) 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) 4.4.12 How many ways can you choose seven people from a group of twenty?

20! / 7!(20-7)! = 2432902008176640000 / 5040(6227050800)

 

5) 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?

 

6) 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?

 

7) 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.)  = 6c1(0.31)1 (1-0.30)6-1 = 6(0.30)(0.7)5 =

 

b.)  = 6c5(0.30)5 (1-0.30)6-5 = 6(0.30)5 (0.7) =

 

c.)  6c3(0.30)3 (1-0.30)6-3 = 20(0.30)3 (0.7)3 =

 

d.)  = 6c0(0.30)0 (1-0.30)6-0+6c1(0.30)1 (1-0.30)6-1+6c2(0.30)2 (1-0.30)6 =

e.)  2 +6c3(0.30)3 (1-0.30)6-3 = 0.117649+0.3025+0.324135+0.18522 =

 

f.)  6c3(0.30)3 (1-0.30)6-3 = 20(0.30)3 (0.7)3 =

 

8) 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.

1. State the random variable.
2. Argue that this is a binomial experiment

This experiment is binomial due to the trials being independent.

N= total number of trials=

 p= probability of success=

 

Find the probability that

3. Six M&M’s are brown.
4. Twenty-five M&M’s are brown.
5. All of the M&M’s are brown.
6.  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?

 

9) 5.3.4

Approximately 10% of all people are left-handed.  Consider a grouping of fifteen people.

1. State the random variable.
2. Write the probability distribution.
3. Draw a histogram.

Lol I don’t know how to insert my Histogram

4. Describe the shape of the histogram.
5. Find the mean.
6. Find the variance.
7. Find the standard deviation.