The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.17 ounces. What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with three of these chocolate bars is between 7.56 and 7.9 ounces? Give your answer to at least 4 decimal places.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.17 ounces.

What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with three of these chocolate bars is between 7.56 and 7.9 ounces? Give your answer to at least 4 decimal places.

 

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Solution:

Let X be the weight of 8=oz chocolate bars produced by a certain machine.

From the given information, X follows normal distribution with mean 7.7 and standard deviation 0.17.

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