Question

Example: 9) An article states that false-positives in polygraph tests (tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about 20% of the time. Suppose that such a test is given to 10 trustworthy individuals. (Round all answers to four decimal places.)

a) What is the probability that all 10 pass?

b) What is the probability that more than 2 fail, even though all are trustworthy?

Example: 9) Suppose that 40% of the students who drive to campus at your university carry jumper cables. Consider the random variable x = number of students who must be stopped before finding a student with jumper cables This is a geometric random variable with p = . Thus the probability distribution of x is p(x) = ( )^x−1 ( ) ^x = 1, 2, 3, . . . Using the above probability distribution find the following probabilities:

a) p(1) =

b) p(2) =

c) P(x ≤ 4) =

c) The article indicated that 500 FBI agents were required to take a polygraph test.

Consider the random variable x = number of the 500 tested who fail.

If all 500 agents tested are trustworthy, what are the mean and standard deviation of x?

Answer 1

Example 9

a) What is the probability that all 10 pass?

The probability that all pass means no one fail.

Probability of failing = 0.20
Probability of passing = 0.80

Using binominal distribution we have

b) What is the probability that more than 2 fail, even though all are trustworthy?

P(more two fail)= 1- (P(0 fail) + P(1 fail) + P(2 fail))

P(more than 2 fails) = 1- (0.1074 + 0.2684+0.302)= 0.3222

c) The article indicated that 500 FBI agents were required to take a polygraph test.

Consider the random variable x = number of the 500 tested who fail.

If all 500 agents tested are trustworthy, what are the mean and standard deviation of x?

mean = 0.20 *(500) = 100
std dev = (0.2) *(0.80)*(500)=80