A cereal manufacturer claims that the gross weight (including packaging) of a box of

Chapter 4, Problem 19

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A cereal manufacturer claims that the gross weight (including packaging) of a box of cereal labeled as weighing \(12 o z \) has a mean of \(12.2 o z\) and a standard deviation of \(0.1 o z\) You gather 75 boxes and weigh them all together. Let S denote the total weight of the 75 boxes of cereal.

a. If the claim is true, what is \(P(S \leq 914.8)\)?

b. Based on the answer to part (a), if the claim is true, is \(914.8 o z\) an unusually small total weight for a sample of 75 boxes?

c. If the total weight of the boxes were \(914.8 o z\), would you be convinced that the claim was false? Explain.

d. If the claim is true, what is \(P(S \leq 910.3)\)?

e. Based on the answer to part (d), if the claim is true, is \(910.3 o z\) an unusually small total weight for a sample of 75 boxes?

f. If the total weight of the boxes were \(910.3 o z\), would you be convinced that the claim was false? Explain.

Equation Transcription:

     

     

   

   

   

   

   

Text Transcription:

12 oz      

12.2 oz      

0.1 oz    

P(S \leq 914.8)    

914.8 oz  

(914.8 oz)    

P(S \leq 910.3)  

910.3 oz

910.3 oz

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