4. Bags of rhinestones that I buy are filled by an automated filling machine, so they...

4. Bags of rhinestones that I buy are filled by an automated filling machine, so they are not perfect. The standard deviation of the number of rhinestones in a bag is 7 rhinestones. Assume that the number of rhinestones in each bag are independent, normal variables.

a) What is the standard deviation of an average number of rhinestones in 25 bags?

b) If the average number of rhinestones is 994, what is the probability that the average fill number of 25 bags is less than 1000.

c) What should the mean fill number of rhinestones be equal to so that the probability that the average of 25 bags is less than 1000 is 0.005.

d) If the mean number of rhinestones is 1009, determine the number of bags that need to be measured such that the probability that the average number of rhinestones is less than 1000 is 0.01.

Expert Solution

orchestra answered 2 years ago

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