An eyeglass manufacturer knows from past experience that 16% of manufactured lenses are defective due to scratches. Suppose that the manufacturer examined seventeen eyeglasses. Assume that the binomial distribution applies. (a) What are the number of trials n and the probability of "success" p in this case? n = 17✓ , P = 0.16 0 Use technology to determine the following probabilities, rounding each to 4 decimal places. (b) Probability that none of the lenses selected have scratches. Answer = 5.16 X (c) Probability that all of the lenses selected have scratches. Answer = 0.1362 X
An eyeglass manufacturer knows from past experience that 16% of manufactured lenses are defective due to scratches. Suppose that the manufacturer examined seventeen eyeglasses. Assume that the binomial distribution applies. (a) What are the number of trials n and the probability of "success" p in this case? n = 17✓ , P = 0.16 0 Use technology to determine the following probabilities, rounding each to 4 decimal places. (b) Probability that none of the lenses selected have scratches. Answer = 5.16 X (c) Probability that all of the lenses selected have scratches. Answer = 0.1362 X
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Transcribed Image Text:An eyeglass manufacturer knows from past experience that 16% of manufactured lenses are defective due
to scratches. Suppose that the manufacturer examined seventeen eyeglasses. Assume that the binomial
distribution applies.
(a) What are the number of trials n and the probability of "success" p in this case?
n = 170, p = 0.16 0
Use technology to determine the following probabilities, rounding each to 4 decimal places.
(b) Probability that none of the lenses selected have scratches.
Answer = 5.16 X
(c) Probability that all of the lenses selected have scratches.
Answer = 0.1362 X
(d) Probability that at least three lenses have scratches.
Answer = 52.66 X
(e) Probability that at most three lenses have scratches.
Answer = 71.59 X
(f) Is it unusual for at least five lenses to be scratched?
Probability of at least five lenses to be scratched = 12.24 X
Because this probability is greater than or equal to
least five lenses scratched.
o 0.05, it is not unusual
o to have at
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