According to a recent survey, the average daily rate for a luxury hotel is $239.51. Assume the daily rate follows a normal probability distribution with a standard deviation of $21.93. Complete parts a through d below.

a. What is the probability that a randomly selected luxury hotel's daily rate will be less than $ 257 question mark

(Round to four decimal places as needed.)

b. What is the probability that a randomly selected luxury hotel's daily rate will be more than $ 266 question mark

(Round to four decimal places as needed.)

c. What is the probability that a randomly selected luxury hotel's daily rate will be between $ 239and $ 259 question mark

(Round to four decimal places as needed.)

d. The managers of a local luxury hotel would like to set the hotel's average daily rate at the 90 th percentile, which is the rate below which 90 %of hotels' rates are set. What rate should they choose for their hotel?The managers should choose a daily rate of $nothing. (Round to the nearest cent as needed.)