Question

A recent study found that 80% of all people over 60 years of age in a large city wear glasses. A random sample of 6 people over 60 years of age is selected.

a. what is the probability that exactly 4 people will wear glasses?

b. what is the probability that at most 5 people will wear glasses?

Answer 1

Solution:

Given n = 6, p = 0.8

q = 1 – p = 1 – 0.8 = 0.2

Part a

We have to find P(X=4)

P(X=x) = nCx*p^x*q^(n – x)

P(X=4) = 6C4*0.8^4*0.2^(6 – 4)

P(X=4) = 15*0.4^4*0.2^2

P(X=4) = 0.01536

Required probability = 0.01536

Part b

We have to find P(X≤5) = 1 – P(X=6)

P(X=x) = nCx*p^x*q^(n – x)

P(X=6) = 6C6*0.8^6*0.2^(6 – 6)

P(X=6) = 1*0.4^6*0.2^0

P(X=6) =0.004096

P(X≤5) = 1 – P(X=6)

P(X≤5) = 1 – 0.004096

P(X≤5) = 0.995904

Required probability = 0.995904