Greater than question and between question for The Sampling Distribution for Proportions

Question

Thank you to whoever helps explain this to me, I tried looking at a few videos and examples from other sites but I can only go as far as P(Z> -7.8921)= 1-(-7.8921)=8.8921 I put in my answer in my homework Saint and it says the answer of 8.8921 is wrong could anyone possibly show me how to do both of these?

Greater than

Based on historical data, your manager believes that 25% of the company's orders come from first-time customers. A random sample of 193 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.24?

Between Than

According to a 2009 Reader's Digest article, people throw away approximately 9% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 73 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.05 and 0.16?

Answer 1

The means will follow a distribution with: μ = .25 and σ = sqrt(p(1-p)/n) = sqrt(.25*.75/193) = .03117

z = (.24-.25)/.03117 = -.3208 The right-hand area = P(z>-.324) = .6258 (Note that the correct way to calculate probability of > z from probability of < z is P(>z) = 1 - P(<z) in this case 1 - .3742 which gives our answer.

Do the same thing for part b except subtract the probability for less than the lower z from the probability of less than the higher z.

You can use the z-calculator at

Z-score Calculator

That will do some of the work for you. You still have to calculate z values though.

Please consider a tutor. Take care.