Doug B. answered • 10/13/15

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Math in Plain Language

First, is the distribution of the sample approximately normal? Yes, n=100 makes this a good approximation even if the population distribution is only slightly bell shaped.

The standard error of a proportion of a sample is given by √(p*q/n) = √[(.2)(.8)/100] = .04.

A z score is calculated using the standard formula z = (x-µ)/σ where σ is the standard error because the question is in regard to the distribution of the sample mean.

1) z = (.22 - .2)/.04 = .02/.04 = 0.5

(Use probability table or calculator for the standard normal distribution)

P(p<.22) = P(Z<0.5) = 0.69146

2) z = (.15 - .2)/.04 = .05/.04 = -1.25

P(p<.15) = P(Z<-1.25) = 0.10565