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According to a research institution, men spent an average of $135.95 on Valentine's Day gifts in 2009. Assume the standard deviation for this population is $45 and that it is normally distributed. A random sample of 20 men who celebrate Valentine's Day was selected. Complete parts a through e.
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than $125?
c. What is the probability that the sample mean will be more than $140?
d. What is the probability that the sample mean will be between $110 and $155?
e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is $135.95.