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Keith_Richards [23]
3 years ago
9

Fifteen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A

hospital has the capacity to handle at most 8 cases of the disease. What is the probability that the hospital’s capacity will be exceeded?a. .146
b. .905
c. .787
d. .854
e. .0950
Mathematics
1 answer:
valina [46]3 years ago
8 0

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 , X\sim Binomial(n=15,p=0.40)

A hospital has the capacity to handle at most 8 cases of the disease.

Binomial distribution formula : P(X=x)= ^nC_xp^x(1-p)^{n-x}

Then , the probability that the hospital’s capacity will be exceeded

P(X>8)=1-P(X\leq8)\\\\=1-0.905\ \ [\text{Using Binomial distribution table for n=15 , x=8 and p=0.4.}]

=0.095

Hence, the probability that the hospital’s capacity will be exceeded is e. .0950.

Thus , the correct option is e. .0950.

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