Question: Assume the room rate for a three-star hotel in a European city follows a normal distribution with a mean of 185 euros and a standard deviation of 16 euros.a. What is the probability that a randomly selected three-star hotel has a room rate ofless than 205 euros?more than 190 euros?exactly 175 euros?between 160 and 191 euros?b. A particular hotel

Assume the room rate for a three$-$star hotel in a European city follows a normal distribution with a mean of $185$ euros and a standard deviation of $16$ euros.

a$.$ What is the probability that a randomly selected three$-$star hotel has a room rate of

less than $205$ euros?

more than $190$ euros?

exactly $175$ euros?

between $160$ and $191$ euros?

b$.$ A particular hotel would like to set its rate so that only $10\%$ of hotels in the city will have lower rates. What room rate should the hotel set?

a$.1.$ The probability is

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

a$.2.$ The probability is

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

a$.3.$ The probability is

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

a$.4.$ The probability is

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

b$.$ The hotel should charge euros.

$($Round to two decimal places as needed.$)$