Question 142057: I need help understanding this problem. I am lost
In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card. (a) Of the next 10 customers, what is the probability that none pay by American Express? (b) At least two? (c) Fewer than three? (d) What is the expected number who pay by American Express? (e) Find the Standard deviation.
Any help would be great. Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card.
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Comment: This is a binomial problem with mean = np = 20*0.2 = 4 and
standard deviation sqrt(npq) = sqrt(20*0.2*0.8) = sqrt(3.2) = 1.7889
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P(pay by AE) = 0.2 ; P(do not pay by AE)= 0.8
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(a) Of the next 10 customers, what is the probability that none pay by American Express?
p(none in 10) = 0.8^10 = 0.10737...
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(b) At least two?
Comment: "at least" is a key word in binomial problems. On this problem
you have to understand the following:
P(none pay) + P(one pays) + P(at least two pay) = 1
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P(at least two) = 1 - [P(none) + P(one pay)
= 1 - [0.10737 + 20C1(0.2)^1*(0.8)^19] = 1 - [0.10737+0.05765] = 0.8350
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(c) Fewer than three?
= P(one) + P(two) = 1- 0.8350 = 0.1650
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(d) What is the expected number who pay by American Express?
mean = np = 20*0.2 = 4
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(e) Find the Standard deviation.
sqrt(npq) = sqrt(4* 0.8) = sqrt(3.2) = sqrt(1.6*2) = 0.8sqrt(2)
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Cheers,
Stan H.
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