Question

Based on the American Chemical Society, there is a 0.9 probability that in 0 the U.S. a randomly selected dollar bill is tainted with traces of cocaine. Assume eight dollar bills are selected at random

a) Find the probability that all of them are tainted with Cocaine

b) Find the probability that the number of dollar bills with traces of cocaine is seven or more

c) Is seven unusually high? Explain why or why not?

Answer 1

So this is a question of binomial distribution.

Let X be the number of bills tainted with traces of cocaine.

Then X ~ Binomial( 8,0.90)

a)

We need to compute Pr(X=8)

b)

c)

Now 7 is not unusually high.

The expected number of bills tainted with cocaine is actually n * p = 8 * 0.90 = 7.2 rounded off to 7

Hence we do expect 7 bills out of 8 to be tainted by cocaine.

Since the probability of 0.90 is so high, therefore we expect the number of bills tainted to be on the higher side.

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