Lie Detector: Suppose a lie detector allows 10% of all lies to go undetected. (a

Question

Lie Detector: Suppose a lie detector allows 10% of all lies to go undetected.

(a) If you take the test and tell 10 lies, what is the probability of having 4 or more go undetected? Round your answer to 3 decimal places.


(b) Would 4 undetected lies be an unusually high number* of undetected lies? Use the criteria that a number (x) is unusually large if P(x or more) 0.05.

Yes, that is an unusually high number of undetected lies.No, that is not an unusually high number of undetected lies.    

...............................................
*Unusually low and high number of successes:
x successes among n trials is an unusually high number of successes if P(x or more) 0.05.
x successes among n trials is an unusually low number of successes if P(x or fewer) 0.05.

Explanation / Answer

P(X=x) = nCx * p^x * (1-p)^n-x

p = 0.1

n=10

P(X >=4) = 1 - P(X <=3)

= 1 - binomdist(3,10,0.1,TRUE)

= 1 - 0.9872

= 0.0128

b)

yes, it is unusually high number since probability is greater than 0.05

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