document.write( "Question 1204513: The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.54 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. What is the probability that the sample mean is less than 2.53 ​inches? \n" ); document.write( "
Algebra.Com's Answer #840806 by Theo(13342)\"\" \"About 
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population mean is 2.54
\n" ); document.write( "population standard deviation is .05
\n" ); document.write( "sample size is 10.
\n" ); document.write( "standard error is standard deviation / sqrt(sample size) = .0158114.
\n" ); document.write( "z = (x - m) / s
\n" ); document.write( "z is the z-score
\n" ); document.write( "x is the sample mean for test
\n" ); document.write( "m is the population mean
\n" ); document.write( "s is the standard error.
\n" ); document.write( "formula becomes z = (2.53 - 2.54) / .0158114 = - .632455.
\n" ); document.write( "area to the left of that z-score under the normal distribution curve is equal to .2635.
\n" ); document.write( "this means probability of the mean of a sample of 10 tennis balls having a diameter less than 2.53 is equal to 26.35%.
\n" ); document.write( "here's what it looks like on a normal distribution calculator.
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