SOLUTION: People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March, 2009). Assume this is the true population proportion and that you plan to take a sample sur

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Question 1028353: People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March, 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior.
What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion? In determining your answer, use the standard error found in part a. and the probability found using the tables in the text.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p = .12 = probability of occurrence
q = 1 - .12 = .88 = probability of not getting the occurrence
n = 540 = sample size
s = sqrt(p*q/n) = sqrt(.12*.88/540) = .01398 = standard error of the distribution of sample means
z1 = -.015/.01398 = -1.07 = the low z-score
z2 = +.015/.01398 = +1.07 = the high z-score
p(z-score is between -1.07 and 1.07) = .7154
looking it up in a z-score table that tells you the area under the normal distribution curve to the left of the indicated z-score, you would get:
z1 area under the distribution curve = .1423
z2 area under the distribution curve = .8577
z2 - z2 area = .8577 - .1423 = .7154.
this agrees with what my calculator told me.
the table i used can be found at the following link.
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf