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# Binomial Distributions

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Suppose that the prevalence of a certain type of tree allergy is 0.42 in the general population. If 100 people randomly chosen from this population are tested for this allergy, what is the probability that exactly 42 of them will have this allergy? Please write your answer as a decimal, precise to at least four decimal places.

Feb 23, 2019

#1
+5782
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$$p[k=42] = \dbinom{100}{42}(0.42)^{42}(1-0.42)^{100-42}\\ \text{I'll let you crunch the numbers}$$

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Feb 23, 2019
#2
+1

That's the formula I was using but I kept calculating wrong or something. Wasn't sure what I was doing wrong.

Guest Feb 23, 2019
#3
+5782
+1

0.08062

Rom  Feb 23, 2019