According to a recent survey by the National Retail Federation, men spent an average of $135.35 on Valentine's Day gifts (compared with $72.28 for women). Assume the standard deviation for this populations if $40 and that it is normally distributed. A random sample of 10 men who celebrate Valentine's Day was selected.
a. Calculate the standard error of the mean
b. What is the probability that the sample mean will be more 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 $120 and $160?
e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is $135.35