Question

1. [4] The prices of condos in a city are normally distributed with a mean of $90,000 and a standard deviation of $28,000.

1. The city government exempts the cheapest 6.68% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?

2. If 1.79% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?

Answer 1

Solution : from the given data mean = =   90,000

standard deviation = =   28,000

Now we have to use standard normal table,

then we have to find the maximun price of condos,

P(Z < z) = 6.68%

P(Z < z) = 0.0668

P(Z < -1.50) = 0.0668

z = -1.50

Now use z-score formula,

x = z * +

x = -1.50 * 28000 + 90000

= 48000

Maximum price = 48000

Here we have to calculate the minimum price of condos

P(Z > z) = 1.79%

1 - P(Z < z) = 0.0179

P(Z < z) = 1 - 0.0179 = 0.9821

P(Z < 2.01)= 0.9821

z = 2.01

Using z-score formula,

x = z * +

x = -2.01 * 28000 + 90000

= 146280

Minimum price = 146280