SOLUTION: It is claimed that 88 percent of first class mail (within the same city) is delivered within two days of the time of mailing. Six letters are randomly sent to different locations.

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Question 876853: It is claimed that 88 percent of first class mail (within the same city) is delivered within two days of the time of mailing. Six letters are randomly sent to different locations.
a) What is the probability that exactly four of them will arrive within two days?

b) What is the probability that at least two will arrive within two days?
Answer by reviewermath(1029) About Me  (Show Source):
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It is claimed that 88 percent of first class mail (within the same city) is delivered within two days of the time of mailing. Six letters are randomly sent to different locations.
X~Binomial(6, 0.88)
a) What is the probability that exactly four of them will arrive within two days?
P(X = 4) = %28matrix%282%2C1%2C6%2C4%29%29%280.88%5E4%29%280.12%5E2%29 = highlight%280.1295%29
b) What is the probability that at least two will arrive within two days?
P(X ≥ 2) = sum%28%28matrix%282%2C1%2C6%2Cx%29%29%280.88%5Ex%29%280.12%5E%286-x%29%29%2Cx+=+2%2C+6%29%29 = highlight%280.9999%29