Answer: e. .0950
Step-by-step explanation:
Let X be the number of people that can be cure from disease.
Since each people independently has a 40% chance of contracting the disease.
So , [tex]X\sim Binomial(n=15,p=0.40)[/tex]
A hospital has the capacity to handle at most 8 cases of the disease.
Binomial distribution formula : [tex]P(X=x)= ^nC_xp^x(1-p)^{n-x}[/tex]
Then , the probability that the hospital’s capacity will be exceeded
[tex]P(X>8)=1-P(X\leq8)\\\\=1-0.905\ \ [\text{Using Binomial distribution table for n=15 , x=8 and p=0.4.}][/tex]
[tex]=0.095[/tex]
Hence, the probability that the hospital’s capacity will be exceeded is e. .0950.
Thus , the correct option is e. .0950.
