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.
Suppose that Liz Williams correctly answered 15 of the 20 questions, which of the following would be a viable conclusion to reach?

a. Because the probability of guessing 15 or more correctly is 0.0207, it is unlikely that she is guessing at the questions and may, in fact, have some special ability.
b. Because the probability of being 15 or more correct is 0.0207, it is likely that she is just guessing at the questions.
c. Because the probability of guessing exactly 15 correct is 0.0148, she must be guessing.
d. If she was guessing, 15 is within one standard deviation of the mean and therefore the must not have any special psychic abilities.

Answer 1

Answer:

b. Because the probability of being 15 or more correct is 0.0207, it is likely that she is just guessing at the questions.

Step-by-step explanation:

-This is a binomial probability distribution with p=0.5, n=20 and x=15.

The function is expressed as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}$

We calculate the probability of guessing 15 or more correctly:

$P(X\geq 15)=1-P(X$

The probability of passing, guessing 15+ correctly, is 0.0207. This probability is very low and it is  it is likely that she is just guessing at the questions