In a telepathy experiment, the "sender" looks at 1 of 5 Zener cards while the "receiver" guesses the symbol. This is repeated 40 times, and the proportion of correct responses is recorded. Because there are 5 cards, we expect random guesses to be right 20% of the time (1 out of 5) in the long run. So in 40 tries, 8 correct guesses, a proportion of 0.20, is common. But of course there will be variability even when someone is just guessing. Thirteen or more correct in 40 tries, a proportion of 0.325, is statistically significant at the 5% level. When people perform this well on the telepathy test, we conclude their performance is not due to chance and take it as an indication of the ability to read minds. In a large experiment with 500 people, how many people do we expect to be identified as telepathic even if everyone is just guessing?
a. 25.
b. 5.
c. 100.
d. it is imposible to estimate.

Now, the central limit theorem states that that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. In simple terms, it means that the sample proportion of a random, independent sample is approximately equal to the population proportion or the overall proportion due to random chance.

Thus;

p = p₀ = 0.20

Expected number of successes from a sample; Mean = μ = np

where;

sample size;n = 500

sample proportion;p = 0.20

Mean;μ= 500 × 0.20 = 100