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 $262 per night. Assume that the standard deviation is unknown.

If 30% of the New York City hotel room rates are more than $282 per night, what is the variance? (Remember the label.)

Please show your work, i would like to learn this!!!

Solution

P ( Z < x ) = 0.3
Value of z to the cumulative probability of 0.3 from normal table is 0.524
P( x-u/s.d < x - 262/s.d ) = 0.3
That is, ( 282 - 262/s.d ) = 0.524
--> s.d = ( 282 - 262 / 0.524 ) = 38.167

Variance = 38.167^2 =    1456.719