Zener cards are often used to test the psychic ability of in

Zener cards are often used to test the “psychic ability” of individuals. In the Zener deck, there are five different patterns displayed, and each has a 1/5 probability of being drawn from a well-shuffled deck. The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted and your very impressive friend guessed right on 41 of those trials. Given this sample, can we use the normal approximation to the binomial?

Solution

we have

p = 41 / 100 = 0.41

and we have n = 100

we can use the normal approximation only if n*p is greater than 5

let see

100 * 0.41 = 41

so n*p is greater than 5

so we can use the normal approximation to the binomial