Answer to Question #266539 in Statistics and Probability for Azeem

Question

A manufacturer of polygraphs lie detector claims that its machines can corrrectly distinguish truthful responses to question 78% of the time if the machine is tested using a set of 60 questions determine the mean and standard deviation for this bernoulli process

Answer 1

Bernoulli proccess is a sequence of independent equally distributed bernoulli random variables

Let X be a random variable represent the amount of correctly distinguished truthful responses, then

$X=X{\scriptscriptstyle 1}+...+X{\scriptscriptstyle 60}$ , where each $X{\scriptscriptstyle 1},...,X{\scriptscriptstyle 60}$ can take value 1 with p = 0.78 and 0 with q = 0.22

Which means that X has binominal distribytion with n = 60, p = 0.78

X ~ Bin(0.78, 60)

The mean of X is $m=0.78 * 60 = 46.8$

The variance is $d = 60 * 0.78 * (1-0.78) = 10.296$

The standard deviation is $\sigma = \sqrt{d}=\sqrt{10.296}\approx3.21$