Question

Suppose it is known that the probability of being susceptible to contract a seasonal flu disease in a town is 0.20. A bio-statistician randomly selected 12 unrelated people from the town and examined if they are susceptible to the disease. Considering upto 4 decimal places, find the following:
(a) expected number of susceptible individuals;
(b) probability that 2 or fewer susceptible individuas;
(c) probability that exactly 3 susceptible individuals;
(d) probability that at least 4 susceptible individuals.

Answer 1

(a). P=0.2,n= 12

$E(x)=np =12\times{0.2}=2.4$

(b). $p(\le2)$

$p(\le2)$ can be obtained from =BINOM.DIST(2,12,0.2,TRUE) excel formula, which yields 0.558346

(c). P=3

P=3 can be obtained from =BINOM.DIST(3,12,0.2,FALSE) excel formula, which yields 0.236223

(d). $P(\ge4)$

$P(\ge4)=1-P(\le3)$

$P(\le3)$ can be obtained from =BINOM.DIST(3,12,0.2,TRUE) excel formula, which yields 0.794569 . thus, $P(\ge4)=1-0.794569=0.205431$