SOLUTION: In the State of OH, 40 percent of all e-mails deal in some way with the depressed U.S. economy. If a random sample of 10 e-mails is selected, what is the probability of the followi

Question 612851: In the State of OH, 40 percent of all e-mails deal in some way with the depressed U.S. economy. If a random sample of 10 e-mails is selected, what is the probability of the following:
Exactly five e-mails deal in some way with the depressed U.S. economy?
Exactly five e-mails do not deal in some way with the depressed U.S. economy?
More than five or less than two e-mails deal in some way with the depressed U.S. economy?
All 10 e-mails deal in some way with the depressed U.S. economy?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In the State of OH, 40 percent of all e-mails deal in some way with the depressed U.S. economy. If a random sample of 10 e-mails is selected, what is the probability of the following:
Binomial Problem with n = 10 and p(depress) = 0.4 ; p(not depress) = 0.6
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Exactly five e-mails deal in some way with the depressed U.S. economy?
P(x=5) = 10C5*0.4*5*0.6^5 = 0.2006
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Exactly five e-mails do not deal in some way with the depressed U.S. economy?
P(x=5) = 10C5*0.6^5*0.4^5 = 0.2006
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More than five or less than two e-mails deal in some way with the depressed U.S. economy?
P(6<= x <=10) + P(0<= x <=1) = [1-binomcdf(10,0.4,5)] + [binomcdf(10,0.4,1)]
= 0.1662 + 0.0464
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= 0.2126
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All 10 e-mails deal in some way with the depressed U.S. economy?
Ans: (0.4)^10 = 0.0001049
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Cheers,
Stan H.
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