Respuesta :
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
=[tex]P(x=26)=100C26(0.26)^{26} (1-0,26)^{100-26}\\ =0.09063\\=0.0906[/tex]
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:
[tex]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[/tex]
