Question

Liz Williams claims to have psychic abilities and predict the future. Anderson Cooper, a CNN personality plans to test her in his famous program called Anderson Coopers 360. The process will entail asking Liz Williams a series of 20 independent questions with yes/no answers. The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge. She will be considered psychic if she correctly answers at least a specified number of the questions (called the cut-off). The cut-off must be set so that the chance of guessing that number or more is no greater than 5 percent. The cut-off value should be:

Answer 1

probability of correctly guessing answer = 1/2 = 0.5

[becAUSE THERE IS ONLY 2 OPTIONS IN WHICH ONE IS CORRECT]

NUMBER of questions asked ,n =20

it is a binomial probability distribution,

and probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

let x be cut off value.

so, P(X≥x) ≤0.05

from binomial probability distribution table ,in cumalative probability

at n=20,p=0.5

we find that

P(X≥14) =0.0577 which is greater than 5%

ans P(X≥15)=0.0207 which is less than 5%

so, cut off value is 15 questions.