Question

The standard deviation of the number of homes sold last year by a group of realtors was 2.5. If Lucas sold 15 homes and his z-score was 1.2, what was the mean number of homes sold?

Answer 1

Lucas's z-score of 1.2 indicates that he sold 15 homes, which was 1.2 standard deviations above the mean number of homes sold by the group of realtors. With a standard deviation of 2.5, we calculated that the mean number of homes sold was 12.

Step-by-step explanation:

To find the mean number of homes sold based on Lucas's z-score and standard deviation, we can use the formula for calculating a z-score, which is:

Z = (X - μ) / σ

Where Z is the z-score, X is the value in question, μ is the mean, and σ is the standard deviation. The question informs us that Lucas has a z-score of 1.2, sold 15 homes, and that the standard deviation (σ) is 2.5. We can input these values into the z-score formula:

1.2 = (15 - μ) / 2.5

We then solve for the mean (μ) as follows:

1.2 * 2.5 = 15 - μ

3 = 15 - μ

μ = 15 - 3

μ = 12

Thus, the mean number of homes sold by the group of realtors last year was 12 homes.