The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of49households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is12.3pounds, what is the probability that the sample mean will be each of the following?

a.More than58pounds

b.More than56pounds

c.Between55and57pounds

d.Less than55pounds

e.Less than47pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)