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Lapatulllka [165]
3 years ago
11

Suppose that the prevalence of a certain type of tree allergy is 0.26 in the general population. If 100 people randomly chosen f

rom this population are tested for this allergy, what is the probability that exactly 26 of them will have this allergy? Please write your answer as a decimal, precise to at least four decimal places.
Mathematics
2 answers:
victus00 [196]3 years ago
8 0

Answer:

The probability that exactly 26 out of 100 randomly selected will have this allergy is P=0.0906.

Step-by-step explanation:

We can model this as a binomial distribution with parameters:

Size n=100

Probability p=0.26.

We can calculate the probability of getting a sample of exactly 26 positives as:

P(X=k)=\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}\\\\P(X=26)=\frac{100!}{26!(100-26)!} 0.26^{26}(1-0.26)^{100-26}\\\\P(X=26)=(6.9957*10^{23})*(6.1561*10^{-16})*(2.1045*10^{-10})\\\\P(X=26)=(6.9957*6.1561*2.1045)*10^{23-16-10}\\\\P(X=26)=90.6329*10^{-3}=0.0906

laiz [17]3 years ago
4 0

Answer:

0.0906

Step-by-step explanation:

Given that the prevalence of a certain type of tree allergy is 0.26 in the general population

X- the no of persons having tree allergy is binomial since each persons is independent of the other and there are two outcomes.

Here n = 100

Required probability = the probability that exactly 26 of them will have this allergy

=P(x=26)=100C26(0.26)^{26} (1-0,26)^{100-26}\\ =0.09063\\=0.0906

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