Question

A management of a factory claims that 70% of all their employees have been vaccinated. If a sample of 15 people are chosen, find probability that more than 13 employees actually get vaccinated.

Answer 1

P(employees who have been vaccinated) = 0.7

Number sample(n) = 15

We need to calculate probability that more than 13 employees actually get vaccinated, i.e. P(X>13) = ?

Here we will use binomial distribution probability which can be calculated as

$P(X=n ; N,p) = {N\choose n}*(p^n)*(1-p)^{(N-n)}\\ P(X>13) = P(X=14)+ P(X=15) = {15\choose14}*(0.7^{14})*(1-0.7)^{(15-14)}\\ + {15\choose15}*(0.7^{15})*(1-0.7)^{(15-15)} = 0.0305 + 0.0047 = 0.0352$

So there is 3.52% probability that more than 13 employees actually get vaccinated.