According to a recent survey, the average daily rate for a luxury hotel is

$238.78. Assume the daily rate follows a normal probability distribution with a standard deviation of $22.89.

Complete parts a through d below.

a. What is the probability that a randomly selected luxury hotel's daily rate will be less than $261?

(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 $268?

(Round to four decimal places as needed.)

c. What is the probability that a randomly selected luxury hotel's daily rate will be between

$244

and $264?

(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

90th 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?

(Round to the nearest cent as needed.)