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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 0.15 ounces.

a. What is the probability that the average weight of a SRS of three of these chocolate bars in between 7.52 and 7.9 ounces? ____
b. For a SRS of three of these chocolate bars, what is the level L such that there is a 1% chance that the average weight is less than L? _____________

User Abligh
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1 Answer

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Final answer:

The question pertains to finding the probability of a sample mean for a normally distributed population and calculating a specific weight level with a given probability for a sample.

Step-by-step explanation:

The question asks for the probability that the average weight of a simple random sample (SRS) of three chocolate bars is between 7.52 and 7.9 ounces when the distribution of weights is normal with a mean of 7.7 ounces and a standard deviation of 0.15 ounces. It also requests the calculation of a specific weight level (L) such that there is a 1% chance that the average weight of a sample of three bars is less than L.

To find the probability that the average weight of three bars is between 7.52 and 7.9 ounces, one would need to use the formulas for the mean and standard deviation of a sampling distribution. The mean of the sampling distribution (the expected value of the sample mean) is the same as the population mean, and the standard deviation is the population standard deviation divided by the square root of the sample size (n).

In the case of the weight level L, we would calculate the z-score corresponding to a 1% probability in the lower tail of the normal distribution and then use it to find the corresponding weight value using the mean and standard deviation of the sample distribution.

User Calco
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