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The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 52 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.4 pounds, what is the probability that the sample mean will be each of the following?

a. More than 59 pounds
b. More than 57 pounds
c. Between 55 and 58 pounds
d. Less than 55 pounds
e. Less than 54 pounds

Round the values of z to 2 decimal places. Round your answer to 4 decimal places, the tolerance is +/-0.0001.
**Round the values of z to 2 decimal places. Round your answer to 4 decimal places.

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