Question

drag the tiles to the correct boxes to complete the pairs. the owner of a real - estate agency is looking over the monthly commission earned by the top three brokers in the past month. she has calculated the mean and standard deviation, sd, of their commissions, in dollars, as shown below:

amanda	benjamin	cathy

|mean = 75,463.12
sd = 3,839.02|mean = 74,124.87
sd = 4,062.50|mean = 76,095.71
sd = 4,227.54|
match each broker with the correct description.
cathy benjamin amanda
had the highest average monthly commission during the past year
68% of their data lie between $71,624.07 and $79,187.37 (1 sd from the mean)
95% of their data lie between $67,785.08 and $84,141.16 (2 sd from the mean)

Explanation:

Step1: Compare the means

We compare the mean commissions of Amanda ($75,463.12$), Benjamin ($74,124.87$) and Cathy ($76,095.71$). Since $76095.71>75463.12 > 74124.87$, Cathy has the highest average monthly - commission.

Step2: Recall the empirical rule for normal distribution

For a normal - distributed data set, about 68% of the data lies within 1 standard deviation (SD) of the mean, and about 95% of the data lies within 2 standard deviations of the mean.
For Amanda:
1 - SD range: Mean $\pm$ SD. $75463.12-3839.02 = 71624.1$ and $75463.12 + 3839.02=79302.14$.
2 - SD range: Mean $\pm2\times$ SD. $75463.12-2\times3839.02=75463.12 - 7678.04 = 67785.08$ and $75463.12+2\times3839.02=75463.12 + 7678.04 = 83141.16$.
So Amanda corresponds to "95% of their data lie between $67785.08$ and $83141.16$ (2 SD from the mean)".
For Benjamin:
1 - SD range: Mean $\pm$ SD. $74124.87-4062.50 = 70062.37$ and $74124.87 + 4062.50=78187.37$.
So Benjamin corresponds to "68% of their data lie between $70062.37$ and $78187.37$ (1 SD from the mean)".

Answer:

Cathy - had the highest average monthly commission during the past year
Benjamin - 68% of their data lie between $70062.37$ and $78187.37$ (1 SD from the mean)
Amanda - 95% of their data lie between $67785.08$ and $83141.16$ (2 SD from the mean)