Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 16.4% defective lenses due to scratches. Suppose Eyeglassomatic examined 12 pairs of eyeglasses. a) State the random variable. Select an answer rv X = the number of 12 randomly selected pairs of eyeglasses that are scratched rv X= the number of randomly selected pairs of eyeglasses that are scratched rv X = a randomly selected pair of eyeglasses that is scratched rv X = a randomly selected pair of eyeglasses rv X = all pairs of eyeglasses that are scratched rv X = is scratched rv X = the probability that a randomly selected pair of eyeglasses is scratched b) List the given numbers with correct symbols. ? X p N n σ s X̄ μ = 12 ? μ σ X̄ p X N s n = 0.164 c) Explain why this is a binomial experiment. Check all that apply. There are more than two outcomes for each pair of eyeglasses Whether or not one randomly selected pair of eyeglasses is scratched will affect whether or not another randomly selected pair of eyeglasses is scratched There are only two outcomes for each pair of eyeglasses Whether or not one randomly selected pair of eyeglasses is scratched will not affect whether or not another randomly selected pair of eyeglasses is scratched There is not a fixed number of pairs of eyeglasses There are a fixed number of pairs of eyeglasses, 12 p = 16.4% remains constant from one randomly selected pair of eyeglasses to another
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 16.4% defective lenses due to scratches. Suppose Eyeglassomatic examined 12 pairs of eyeglasses.
a) State the random variable.
Select an answer rv X = the number of 12 randomly selected pairs of eyeglasses that are scratched rv X= the number of randomly selected pairs of eyeglasses that are scratched rv X = a randomly selected pair of eyeglasses that is scratched rv X = a randomly selected pair of eyeglasses rv X = all pairs of eyeglasses that are scratched rv X = is scratched rv X = the probability that a randomly selected pair of eyeglasses is scratched
b) List the given numbers with correct symbols.
? X p N n σ s X̄ μ = 12
? μ σ X̄ p X N s n = 0.164
c) Explain why this is a binomial experiment. Check all that apply.
- There are more than two outcomes for each pair of eyeglasses
- Whether or not one randomly selected pair of eyeglasses is scratched will affect whether or not another randomly selected pair of eyeglasses is scratched
- There are only two outcomes for each pair of eyeglasses
- Whether or not one randomly selected pair of eyeglasses is scratched will not affect whether or not another randomly selected pair of eyeglasses is scratched
- There is not a fixed number of pairs of eyeglasses
- There are a fixed number of pairs of eyeglasses, 12
- p = 16.4% remains constant from one randomly selected pair of eyeglasses to another
Find the probability, to 4 decimal places:
It is possible when rounded that a probability is 0.0000
d) exactly none are scratched.
e) exactly 8 are scratched.
f) at least 5 are scratched.
g) at most 6 are scratched.
h) at least 6 are scratched.
i) Is 6 an unusually high number of pairs of eyeglasses that are scratched in a sample of 12 pairs of eyeglasses?
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