please help will rate The hotel room rate in New York City i

please help will rate

The hotel room rate in New York City is normally distributed with a mean of $231 per night. Assume that the standard deviation is unknown.

If 25% of the New York City hotel room rates are more than $261 per night, what is the variance? (Remember the label.)

Solution

Here, the left tailed area for 261 is 1-0.25 = 0.75.

Thus, the corresponding z score to it is

z = 0.67448975

As

z = (x - u) / sigma

Then

sigma^2 = variance = [(x-u)/z]^2

Thus,

variance = ((261-231)/0.67448975)^2 = 1978.298406 $^2 [ANSWER]