I'm stuck on the latter part of this equation, for some reason I got a 12 for the .4 proportion when I attempted to standardize it. This does not correlate with my z distribution chart. Thanks!

Question

Based on historical data, your manager believes that 25% of the company's orders come from first-time customers. A random sample of 224 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.27 and 0.4?

Answer 1

Because this is a proportion, the σ = sqrt(p(1-p)/n) = .02893

The 2 z values are: obtained by plugging in the limits of the interval .27 and .4 for x in

z = (x-p)/σ z(.4) = (.4-.25)/.02893) = 5.185 z(,27) = .691

Look up the probabilities for the z values and take the difference.