A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing.

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A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines) and the person being tested has to predict the shape on each card before it is selected. Answer questions a-c below to find each of the probabilities requested for a person who has no ESP and is just guessing. a. Determine the statistical procedure you should use to answer this question and explain why. b. What is the probability of correctly predicting exactly 20 cards in a series of 100 trials? c. What is the probability of correctly predicting more than 16 cards in a series of 64 trials?

Step-by-step explanation:

a)

X - the number of success

following the binomial distribution with p = 1/5

or when np > 5 ,nq > 5

we can use normal approximation

mean = np

sd =sqrt(npq)

b)

here n = 100

P(X = k) = 100Ck * (1/5)^k *(1-1/5)^(100-k)

P(X = 20) = 100C20 (1/5)^20* (4/5)^80

by normal approximation

μ = 20 and σ = 4 For X = 20,

P(19.5 < X< 20.5)

P ( −0.13<Z<0.13 )=0.1034

and p = 0.1034.

c)

P(X > 16)

mean = np = 64/5 = 12.8

sd = sqrt(npq) = sqrt(12.8*.8)= 3.2

P(X > 16)

=P(Z > (16.5 - 12.8)/3.2)

= P(Z> 1.1562)

= 0.1238