document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #643474 by Theo(13342)\"\" \"About 
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p = .12 = probability of occurrence
\n" ); document.write( "q = 1 - .12 = .88 = probability of not getting the occurrence
\n" ); document.write( "n = 540 = sample size
\n" ); document.write( "s = sqrt(p*q/n) = sqrt(.12*.88/540) = .01398 = standard error of the distribution of sample means
\n" ); document.write( "z1 = -.015/.01398 = -1.07 = the low z-score
\n" ); document.write( "z2 = +.015/.01398 = +1.07 = the high z-score
\n" ); document.write( "p(z-score is between -1.07 and 1.07) = .7154
\n" ); document.write( "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:
\n" ); document.write( "z1 area under the distribution curve = .1423
\n" ); document.write( "z2 area under the distribution curve = .8577
\n" ); document.write( "z2 - z2 area = .8577 - .1423 = .7154.
\n" ); document.write( "this agrees with what my calculator told me.
\n" ); document.write( "the table i used can be found at the following link.
\n" ); document.write( "http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
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