Zener cards are often used to test the “psychic ability” of individuals. In the

Question

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? yes, because np 10 no, because np 10 and n(1 – p) 10 no, because n(1 – p) 10 yes, because np 10 and n(1 – p) 10 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? yes, because np 10 no, because np 10 and n(1 – p) 10 no, because n(1 – p) 10 yes, because np 10 and n(1 – p) 10

Explanation / Answer

A binomial approximation to a normal distribution can be made is

np > 10 and n(1-p) > 10

Here, n = 100

np = 100 * 0.2 = 20 > 10

n ( 1-p) = 100 * 0.8 = 80

variance = np(1-p) = 80 * 0.2 = 16

Hence,

the given sample can be approximated to a normal distribution

Option D is correct.

Hope this helps.

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