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Suppose that the prevalence of a certain type of tree allergy is 0.17 in the general population. If 100 people randomly chosen from this population are tested for this allergy, what is the probability that exactly 17 of them will have this allergy

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Answer:

The probability that exactly 17 of the people will have the allergy is 0.1057.

Step-by-step explanation:

Let X be the emount of people with allergy in the sample of 100 people. X has a binomial distribution with paramenters n = 100, p = 0.17. The probability of X being 17 is

[tex]P(X=17) = {100 \choose 17} * 0.17^{17} * 0.83^{83} = 0.1057[/tex]

The probability that exactly 17 of the people will have the allergy is 0.1057.

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