# Vending Machines Quarters are now manufactured so that they have a mean weight of 5.670 g and a standard deviation of 0.062 g, and their weights are normally distributed. A vending machine is configured to accept only those quarters that weigh between 5.550 g and 5.790 g.a. If 1 randomly selected quarter is inserted into the vending machine, what is the probability that it will be accepted?b. If 4 randomly selected quarters are inserted into the vending machine, what is the probability that their mean weight is between 5.550 g and 5.790 g?c. If you own the vending machine, which result is more important: the result from part (a) or part (b)?

Question
Asked Jan 17, 2020
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Vending Machines Quarters are now manufactured so that they have a mean weight of 5.670 g and a standard deviation of 0.062 g, and their weights are normally distributed. A vending machine is configured to accept only those quarters that weigh between 5.550 g and 5.790 g.

a. If 1 randomly selected quarter is inserted into the vending machine, what is the probability that it will be accepted?

b. If 4 randomly selected quarters are inserted into the vending machine, what is the probability that their mean weight is between 5.550 g and 5.790 g?

c. If you own the vending machine, which result is more important: the result from part (a) or part (b)?

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## Expert Answer

Step 1

a)

The random variable x represents weights of quarters.

The formula to convert the weights of quarters into z scores is,

Step 2
Step 3

The probability that is accepted if 1 randomly selected quarter is inserted into the vending machine is obtained by finding the difference be...

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