According to a research Institution, the average hotel price in a certain year was $106.72. Assume the population standard deviation is $25.00 and that a random sample of 50 hotels was selected. Complete parts a through d below. a. Calculate the standard error of the mean $3.54 (Round to two decimal places as needed.) b. What is the probability that the sample mean will be less than $1097 P(x$112) - (Round to four decimal places as needed.) d. What is the probability that the sample mean will be between $105 and $107? P($1055&s $107) (Round to four decimal places as needed.)