Question

The Lake Geneva business council has collected data on the vacationers visiting their township. For a typical 3-day weekend, the average family of four will spend $1020 with a standard deviation of $110. Find the Z-Scores for the following families of four:

a) Z-Score for a family spending $910
b) Z-Score for a family spending $1050
c) Z-Score for a family spending $1155

Answer 1

The Z-Scores for the families spending $910, $1050, and $1155 are -1, 0.27, and 1.23, respectively. These scores show how much each family's spending deviates from the average.

Step-by-step explanation:

The question asks us to calculate the Z-Scores for families of four spending different amounts of money during a typical 3-day weekend.

To find the Z-Score, we use the formula:

Z = (X - μ) / σ

where X is the spending of the family, μ is the mean spending, and σ is the standard deviation.

• For a family spending $910: Z = ($910 - $1020) / $110 = -1
• For a family spending $1050: Z = ($1050 - $1020) / $110 = 0.27
• For a family spending $1155: Z = ($1155 - $1020) / $110 = 1.23

These Z-Scores indicate how many standard deviations each family's spending is from the mean.