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Eyeglassomatic manufactures eyeglasses for different retailers

04/01/2021 Client: saad24vbs Deadline: 10 Days

Section 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.


Section 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


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.


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?


Section 4.4


6.) Find 10P6


12.) How many ways can you choose seven people from a group of twenty?


Section 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 for to flip two heads?


4.) An LG Dishwasher has a 20% chance of needing to be repaired in the first 9 years


of purchase. A two-year extended warrantee costs $112.10 on a dishwasher.


What is the expected value of the extended warranty?


Section 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)


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?


Section 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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