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According to a recent​ survey, the average daily rate for a luxury hotel is ​$232.84. Assume...

According to a recent​ survey, the average daily rate for a luxury hotel is ​$232.84. Assume the daily rate follows a normal probability distribution with a standard deviation of ​$22.92. Complete parts a through d below.

a. What is the probability that a randomly selected luxury​ hotel's daily rate will be less than $ 245?

​(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 $ 258?

​(Round to four decimal places as​ needed.)

c. What is the probability that a randomly selected luxury​ hotel's daily rate will be between $243 and $263?

​(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 80th

​percentile, which is the rate below which 80​% of​ hotels' rates are set. What rate should they choose for their​ hotel?

The managers should choose a daily rate of ________.

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