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4.18 Chicken Pox, Part I: The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.[National Vaccine Information Center]

(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distribution appropriate for calculating the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood?

No, the normal distribution should be used
Yes, there are 100 independent trials, each with exactly two possible outcomes, and a constant probability associated with the outcomes in each trial
No, the trials are not independent
No, this follows the bimodal distribution

(b) Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.
(please round to four decimal places)

(c) What is the probability that exactly 3 out of a new sample of 100 American adults have not had chickenpox in their childhood?
(please round to four decimal places)

(d) What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox? (please round to four decimal places)

(e) What is the probability that at most 3 out of 10 randomly sampled American adults have had chickenpox?
(please round to four decimal places)

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