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The accompanying table contains the results from experiments with a polygraph in

ID: 3129949 • Letter: T

Question

The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts a) and b) below. Are these events unlikely?

No (did not lie) Yes (lied)

Positive test result 7 false positive36 true positive

(Positive test indicated that the subject lied)

Negative test results 60 (true negative) 11 False negative

(Polygraph test indicated that the subject did not lie)

a) The probability that all four test subjects had a true negative test result when they are randomly selected with a replacement is _______________round to three decimals places as needed.

Is such an event unlikely?

A) Yes because the probability of the event is less than 0.05

B) No because the probability of the event is less than 0.05

C) Yes because the probability of the event is greater than 0.05

D) No, becuase the probability of the event is greater than 0.05

b)The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is _____________________round to three decimal places as needed

A)

Explanation / Answer

a)

There are 7+60+36+11 = 114 participants here, where 60 have true negatives.

Hence,

P(true negative) = 60/114 = 0.526315789

Hence,

P(all 4 true negative) = 0.526315789^4 = 0.076733604 [ANSWER]

Hence,

OPTION D: D) No, becuase the probability of the event is greater than 0.05 [ANSWER]

*************************

b)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    114      
K = number of successes in the population =    60      
n = sample size =    4      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.073077186 [ANSWER]

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