Question

According to the Centers for Disease Control, between 5% and 20% of people in the US get influenza each year. Suppose that this year, 20% of people get influenza.

a. If you take a random sample of 10 people, what’s the probability that exactly 2 of them get influenza?

b. If you take a random sample of 10 people, what’s the probability that at most 7 of them do not get influenza?

Answer 1

here this is binomial with parameter n=10 and p=0.2

a)

probability that exactly 2 of them get influenza:

P(X=2)=

(10C2)0.22(1−0.2)(10-2)    =

0.3020

b)

probability that at most 7 of them do not get influenza =P(at least 3 get the influenza):

P(X>=3)=1-P(X<=2)=

1-∑x=02   (10Cx)0.2x(0.8)(n-x) =

0.3222