document.write( "Question 1169033: The mean amount purchased by a typical customer at PQR Store is $21.60 with standard deviation of $8.80. Assume the distribution of amount purchase follows the normal probability. For a sample of 64 customers, what is the probability the sample mean is less than $20.00? \n" ); document.write( "
Algebra.Com's Answer #793919 by Theo(13342)\"\" \"About 
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population mean is 21.60
\n" ); document.write( "population standard deviation is 8.80
\n" ); document.write( "sample size is 64 customers.
\n" ); document.write( "probability sample mean is less than 20.00 is what?\r
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\n" ); document.write( "\n" ); document.write( "standard error = standard deviation / square root of sample size.
\n" ); document.write( "standard error = 8.80/sqrt(64) = 8.80/8 = 1.10\r
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\n" ); document.write( "\n" ); document.write( "z-score = (x-m)/s
\n" ); document.write( "x is the raw score
\n" ); document.write( "m is the mean
\n" ); document.write( "s is the standard error.\r
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\n" ); document.write( "\n" ); document.write( "in this problem, .....
\n" ); document.write( "z-score = (20 - 21.60) / 1.10
\n" ); document.write( "solve for z-score to get:
\n" ); document.write( "z = -1.454545.....
\n" ); document.write( "round to -1.45\r
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\n" ); document.write( "\n" ); document.write( "area to the left of a z-score of -1.45 is be equal to .0735.
\n" ); document.write( "that's the probability that the sample mean will be less than 20.00.\r
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