SOLUTION: The United States Postal Service reports 95% of first class mail within the same city is delivered within two days of the time of the mailing. Six letters are randomly sent to diff

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Question 198560: The United States Postal Service reports 95% of first class mail within the same city is delivered within two days of the time of the mailing. Six letters are randomly sent to different locations
a) What is the probability all six arrive within two days?
b) What is the probability that exactly five arrive within two days?
c) Find the mean number of letters that will arrive within two days
d) Compute the variance and Standard Deviation of the number that will arrive within two days.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The United States Postal Service reports 95% of first class mail within the same city is delivered within two days of the time of the mailing. Six letters are randomly sent to different locations
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a) What is the probability all six arrive within two days?
Ans: (0.95)^6 = 0.735
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b) What is the probability that exactly five arrive within two days?
Ans: 6C5(0.95)^5(0.05)^1 = 0.2321
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c) Find the mean number of letters that will arrive within two days
Ans: u = np = 6*0.95 = 5.7
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d) Compute the variance and Standard Deviation of the number that will arrive within two days.
Ans: variance = npq = 6*0.95*0.05 = 0.285
stdev = sqrt(0.285) = 0.5339
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Cheers,
Stan H.