A federal report find that a lie detector test given to trut

A federal report find that a lie detector test given to truthful persons have a probability of 0.2 of suggesting that the person is deceptive. A compan asks 12 job applicants to take a lie detect test. Suppose that all 12 applicants answer truthfully.

What is the probablilty that exactly one is being deceptive.

What is the probability that at most one is being deceptive.

What is the mean and standard deviation of this distribution.

Solution

The question is type of binomial distribution
a) Proabability of exactly one deceptive is = 12C1*0.2*0.8^11

b) Probability of atmost 1 being deceptive = probability of 1 + 0 being deceptive = 12C0 *0.8^12 +12C1*0.2*0.8^11

c) Mean= probability *no of trials = 0.2*12 = 2.4
Standard deviation = n * P * ( 1 - P ) = 12*0.2*0.8 = 1.92