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 the 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.


Amanda

Benjamin

Cathy

Which broker had the highest average monthly

commission during the past year?

arrowBoth

For which broker does 95% of the data lie

between $67,785.08 and $83,141.16

(2 SD from the mean)?

arrowBoth

For which broker does 68% of the data lie

between $70,062.37 and $78,187.37

(1 SD from the mean)?

arrowBoth

Answer 1

68% of their data lie between $70,062.37 and $78,187.37

(1 SD from the mean) Benjamin

had the highest average monthly commission during the past year Cathy

95% of their data lie between $67,785.08 and $83,141.16

(2 SD from the mean) Amanda

Explanation:

Answer 2

• highest mean: Cathy
• 2SD limits given: Amanda
• 1 SD limits given: Benjamin

Explanation:

This problem is essentially one of finding the matching mean. The given means are ...

• A: 75,463.12
• B: 74,124.87
• C: 76,095.71

1. It should be no trouble to determine that the largest mean belongs to Cathy.

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2. The mean is the average of the given 2SD limits, so is ...

(67,785.08 +83,141.16)/2 = 75,463.12 . . . . matches Amanda

Please note that you only need to work with about 3 significant figures:

(67.8 +83.1)/2 = 75.45 . . . . close enough to let you select Amanda

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3. The mean is the average of the given 1SD limits, so is ...

(70.1 +78.2)/2 = 74.15 . . . . matches Benjamin