Question

15) Suppose the probability of contracting a certain disease is 1 in 43,093 for a new case in a given year. Approximate the probability that in a town of 2,504 people there will be at least one new case of the disease next year. Express your answer as a percentage rounded to the nearest hundredth.

16) A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates there is a 91% probability that the calculator will work on any given day. Because the final exam is so important, she plans to bring in two calculators in case one loses power. Does she gain much by bringing in the backup calculator? Use the probability that she will be able to complete her exam with a working calculator.

Answer 1

15)
mean = 2504 * 1/43093
= 0.0581

X follow poisson distribution
P(X >= 1) = 1- P(X = 0)
= 1- e^(-mean)
= 1- e^(-0.0581)
= 0.05644

we can solve using binomial distribution too

P(X >= 1) = 1- P(X = 0)

= 1-(1-1/43093)^2504

= 0.05645

we see that both probabilities are equal

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