According to the USA Snapshot Knowing drug addicts 40 of Ame

According to the USA Snapshot “Knowing drug addicts” 40% of Americans know somebody who became addicted to a drug other than alcohol. Assuming this to be true, what is the probability that out of a group of 20 randomly selected Americans: a. Exactly 10 know somebody who became addicted to a drug? b. At most 10 know somebody who became addicted to a drug? c. More than 10 know somebody who became addicted to a drug?

Solution

Solution:

Case of binomial distribution.

Here n=sample size=20

p=probability of success=40%=40/100=0.40

q=probability of failure=1-p=1-0.4=0.6

Binomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:

b(x; n, P) = _nC_x * P^x * (1 - P)^{n - x}

(a)

P(Exactly 10 know somebody who became addicted to a drug)=

P(x = 10) = binompdf(10,20,0.4) 20_C10 (0.4)¹⁰(0.6)^20-10 0.1171

(b)

P(At most 10 know somebody who became addicted to a drug)=

  P(x 10) = binomcdf(10,20,0.4) =0.8725

(c)

P( More than 10 know somebody who became addicted to a drug)=P(x 11)

P(x 11)=1- P(x 10)

=1 - 0.8725

=0.1275