document.write( "Question 856925: Question 2.3 - To ensure that Head & Shoulders shampoo is not over or under filling its 500ml
\n" ); document.write( "bottles, the company maintains records regarding the amount in each 500ml bottle. The records
\n" ); document.write( "indicate that the amount of shampoo in each bottle follows a normal probability distribution. The
\n" ); document.write( "mean amount of shampoo per bottle is 500.2ml and the population standard deviation is 0.8ml. A
\n" ); document.write( "technician selects a sample of 36 bottles from the filling line. The mean amount of shampoo
\n" ); document.write( "contained in the sample of bottles is 500.7ml.
\n" ); document.write( "Apply the Central Limit Theorem to investigate if this is an unlikely result? \n" ); document.write( "
Algebra.Com's Answer #516232 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!
 
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document.write( "Hi,
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document.write( "Population s = .8/sqrt(36) = .8/6 = .1333
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document.write( "z = (500.7 - 500.2)/.133 = .5/.1333 = 3.751
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document.write( " 3.75 standard deviations from mean?  YES unlikely\r
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document.write( "For the normal distribution: 
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document.write( "one  standard deviation from the mean accounts for about 68.2% of the set 
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document.write( "two standard deviations from the mean account for about 95.4%
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document.write( "and three standard deviations from the mean account for about 99.7%.
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document.write( "Important to Understand z -values as they relate to the Standard Normal curve:
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document.write( "Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  
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document.write( "Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right
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