The hotel room rate in New York City is normally distributed

The hotel room rate in New York City is normally distributed with a mean of $229 per night. Assume that the standard deviation is unknown.

Question: If 21% of the New York City Hotel room rates are more than $264 per night, what is the variance?

Please Explain how to set up.

Solution

The critical z score for the top 21% is

zcrit = 0.806421247

As

z = (x - u) / sigma

Then

sigma = (x - u) / z

Then

sigma = (264-229)/0.806421247 = 43.40163423 [answer]