A cereal manufacturer claims that the weight of a box of cereal labeled as weighing 12 ounces has a mean of 12.0 ounces and a standard deviation of 0.1 ounce. You sample 75 boxes and weigh them. Let line over x symbol denote the mean weight of the 75 boxes. a) If the mean weight of the boxes were 11.99 ounces, would you be convinced that the claim was false? Explain. b) Is 11.99 ounces an unusually small mean weight for a sample of 75 boxes?c) If the mean weight of the boxes wre 11.97 ounces, would you be convinced that the claim was false? Explain.

Question
Asked Apr 30, 2019
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A cereal manufacturer claims that the weight of a box of cereal labeled as weighing 12 ounces has a mean of 12.0 ounces and a standard deviation of 0.1 ounce. You sample 75 boxes and weigh them. Let line over x symbol denote the mean weight of the 75 boxes. 

a) If the mean weight of the boxes were 11.99 ounces, would you be convinced that the claim was false? Explain. 

b) Is 11.99 ounces an unusually small mean weight for a sample of 75 boxes?

c) If the mean weight of the boxes wre 11.97 ounces, would you be convinced that the claim was false? Explain. 

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Expert Answer

Step 1

In this question, it has been given that A manufacturer claims that weight of cereal follows the Normal distribution with mean is equal to 12 ounces and standard deviation is equal to 0.1 ounce.

Using this information, we have to answer the questions;

Step 2

a) If the mean weight of the boxes were 11.99 ounces, would you be convinced that the claim was false? Explain. 

Calculation have shown on whiteboard:

Since the probability of mean weight were less than equal to 11.99 is equal to 0.1922. This shows that it’s not an unusual event of having the weight 11.99 ounces.

Therefore, Yes, I am convinced that the claim that mean weight is equal to 12 ounces.

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Step 3

b) Is 11.99 ounces an unusually small mean weight for a sample of 75 boxes?

No, it’s not unusually small that mean weight for a samp...

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