Ms. Ramírez is a real estate broker. Last month, the sale prices of homes in her area approximated a normal distribution with a mean of $150,000 and a standard deviation of $25,000. What is the probability that the sale is less than $175,000?(1 point)

Question

The probability that the sale is less than $175,000 is
%.

Answer 1

To find the probability that the sale price of homes is less than $175,000, we can use the properties of the normal distribution.

1. Identify the mean and standard deviation:

   • Mean (\(\mu\)) = $150,000
   • Standard deviation (\(\sigma\)) = $25,000

2. Convert the sale price to a z-score: The z-score is calculated using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \(X\) is the value we are interested in ($175,000).

   Substituting the values: \[ z = \frac{(175,000 - 150,000)}{25,000} = \frac{25,000}{25,000} = 1 \]

3. Look up the z-score in the standard normal distribution table or use a calculator. The z-score of 1 corresponds to a cumulative probability of approximately 0.8413.

4. Convert the probability to a percentage: \[ 0.8413 \times 100 = 84.13% \]

Therefore, the probability that the sale is less than $175,000 is approximately 84.13%.