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?
A)Yes, because np $\ge$10.
B)Yes, because np$\ge$10 and n(1 - p)$\ge$ 10.
C)No, because n(1 - p)$\ge$10.
D)No, because np$\ge$ 10 and n(1 - p)$\ge$ 10.

Question

Quizplus · Accepted Answer

The Normal approximation to the binomial can be used when np and n(1-p) are both greater than or equal to 10. In this case, np = 100*(1/5) = 20 and n(1-p) = 100*(4/5) = 80, both of which are greater than 10. Therefore, the Normal approximation can be used, and the conditions for using it are met.

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