According to a researchinstitution, men spent an average of $134.83 onValentine'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 celebrateValentine's Day was selected. Complete parts a through e.

a. Calculate the standard error of the mean.

x=

(Round to two decimal places asneeded.)

b. What is the probability that the sample mean will be less than $130?

Px<$130=

(Round to four decimal places asneeded.)

c. What is the probability that the sample mean will be more than $140?

Px>$140=

(Round to four decimal places asneeded.)

d. What is the probability that the sample mean will be between $110 and $165?

P$110x$165=

(Round to four decimal places asneeded.)

e. Identify the symmetrical interval that includes95% of the sample means if the true population mean is $134.83.

$

x$

(Round to the nearest dollar asneeded.)