A quality-control program at a plastic bottle production line involves inspecting finished bottles for flaws such as microscopic holes. The proportion of bottles that actually have such a flaw is only 0.0002. If a bottle has a flaw, the probability is 0.991 that it will fail the inspection. If a bottle does not have a flaw, the probability is 0.98 that it will pass the inspection. A) If a bottle fails inspection, what is the probability that it has a flaw?
B) Which of the following is the more correct interpretation of the answer to part (a)?
1) Most bottles that fail inspection do not have a flaw
2) Most bottles that pass inspection do have a flaw
C) If a bottle passes inspection, what is the probability that it does not have a flaw?
D) Which of the following is the more correct interpretation of the answer to part (c)?
1) Most bottle that fail inspection do have a flaw
2) Most bottles that pass inspection do not have a flaw
E) Explain why a small probability in part (a) is not a problem, so long as the probability in part (c) is large.

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step-by-step explanation:

10.4 inches

step-by-step explanation:

2x2x2.6

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.