Based on the American Chemical Society, there is a 0.9 probability that in the U

Question

  Based on the American Chemical Society, there is a 0.9 probability that in the United States, a randomly selected dollar bill is tainted with traces of cocaine. Assume that eight dollar bills are randomly selected, find the following:

a) Find the probability that all of them have traces of cocaine.

b) Find the probability that exactly 7 of them have traces of cocaine.

c) Find the probability that at least 7 of the bills have traces of cocaine.

d) Find the probability that less than 7 of the bills have traces of cocaine.

e) Find the mean, variance, and standard deviation of this distribution.

Explanation / Answer

p=0.9 q=0.1

a) p(x=8)

8c8*0.9^8*0.1^0

=0.43046

b)P(x=7)

8c7 0.9^7 0.1^1

=0.38263752

c)p(7+8) = p(7)+p(8)

=0.38263752+ 0.43046

=0.81310473

d)p(x<7) =1-P(x>7)

=1-0.81310473

=0.18689527

e) mean =np =7.2

variance =npq =8*0.9*0.1 =0.72

standard deviation = square root npq = 0.848528137

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