7.17 According to a recent survey by the National Retail Federation, men spent an average of $135.35 on Valentines 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 Valentines 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