SOLUTION: Question 2.3 - To ensure that Head & Shoulders shampoo is not over or under filling its 500ml bottles, the company maintains records regarding the amount in each 500ml bottle. Th

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Question 856925: Question 2.3 - To ensure that Head & Shoulders shampoo is not over or under filling its 500ml
bottles, the company maintains records regarding the amount in each 500ml bottle. The records
indicate that the amount of shampoo in each bottle follows a normal probability distribution. The
mean amount of shampoo per bottle is 500.2ml and the population standard deviation is 0.8ml. A
technician selects a sample of 36 bottles from the filling line. The mean amount of shampoo
contained in the sample of bottles is 500.7ml.
Apply the Central Limit Theorem to investigate if this is an unlikely result?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Population s = .8/sqrt(36) = .8/6 = .1333

z = (500.7 - 500.2)/.133 = .5/.1333 = 3.751

 3.75 standard deviations from mean?  YES unlikely



For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right