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
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"
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