Question

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1. Several psychology students are unprepared for a surprise true/false test with 8 questions, and all of their answers are guesses.

1. μ=
2. σ=
3. Would guessing and getting at least 6 questions correct be unusual? Why or why not?

Answer 1

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This is an application of binomial distribution. The parameters of the binomial distribution are:

n = 8

p = .50

a. Mu = the mean is n*p = 8*.5 = 4

b. Sigma = standard deviation = sqrt(n*p*q) = sqrt(8*.5*.5) = 1.4142

c. P(X>=6) = 1- P(X<=5) = 1-0.8555 = 0.1445. Since this is not less than .05 ( usual threshold below which an event is considered unsual), we conclude that getting atleast 6 is NOT UNUSUAL.