Question

A construction company in Florida is struggling to sell condominiums. The company believes that it will be able to get an average sale price of $323,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $20,000. [You may find it useful to reference the z table.]

a. What is the probability that the condominium will sell at a price
(i) Below $302,000?
(ii) Above $357,000? (Round your final answers to 4 decimal places.) Below $302,000 Above $357,000 Probability
b. The company is also trying to sell an artist's condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $323,000, but with a higher standard deviation of $23,000. What is the probability that this condo will sell at a price
(i) Below $302,000?
(ii) Above $357,000? (Round your answers to 4 decimal places.) Below $302,000 Above $357,000 Probability

Answer 1

The probability that the condominium will sell below $302,000 is approximately 0.1469 and the probability that it will sell above $357,000 is approximately 0.9554. For the artist's condo, the probability of selling below $302,000 is approximately 0.1802 and the probability of selling above $357,000 is approximately 0.9292.

Step-by-step explanation:

a.

To find the probability that the condominium will sell at a price below $302,000, we need to calculate the z-score using the formula:
z = (x - μ) / σ
Where x is the price, μ is the mean price, and σ is the standard deviation. In this case, x = $302,000, μ = $323,000, and σ = $20,000.

Plugging in the values, we get:
z = ($302,000 - $323,000) / $20,000 = -1.05

Using the z-table, we can find the probability associated with the z-score of -1.05, which is 0.1469.

Therefore, the probability that the condominium will sell at a price below $302,000 is approximately 0.1469.

To find the probability that the condominium will sell at a price above $357,000, we can follow the same steps as above. Plugging in the values, we get:
z = ($357,000 - $323,000) / $20,000 = 1.7

Using the z-table, we can find the probability associated with the z-score of 1.7, which is 0.9554.

Therefore, the probability that the condominium will sell at a price above $357,000 is approximately 0.9554.

b.

If the standard deviation for the artist's condo is $23,000 instead of $20,000, we follow the same steps as above to find the probabilities. Plugging in the values for the first case, we get:
z = ($302,000 - $323,000) / $23,000 = -0.913

Using the z-table, we find the probability associated with the z-score of -0.913, which is 0.1802.

Therefore, the probability that the artist's condo will sell at a price below $302,000 is approximately 0.1802.

Plugging in the values for the second case, we get:
z = ($357,000 - $323,000) / $23,000 = 1.478

Using the z-table, we find the probability associated with the z-score of 1.478, which is 0.9292.

Therefore, the probability that the artist's condo will sell at a price above $357,000 is approximately 0.9292.