A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces

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Tue May 11, 2021 5:16 pm

GMAT Prep

7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53

A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

A. Four
B. Six
C. Nine
D. Ten
E. Eleven

OA E

If the Standard Deviation is 0.3 ounces, then 0.3 ounces represents 1 unit of standard deviation.
Similarly, 0.6 ounces represents 2 units of standard deviation,
0.15 ounces represents 0.5 units of standard deviation, and so on.

If the mean is 8.1 ounces, then we say that 8.4 ounces is 1 unit of standard deviation above the mean (since 8.1 + 0.3 = 8.4), and we say that 7.8 ounces is 1 unit of standard deviation below the mean (since 8.1 - 0.3 = 7.8)

We want to know how many measurements in the list are within 1.5 standard deviations of the mean

Well, using the above logic, 0.45 represents 1.5 units of standard deviation.

So, 1.5 units of standard deviation below the mean equals 7.65 (8.1 - 0.45 = 7.65)
Similarly, 1.5 units of standard deviation abovethe mean equals 8.55 (8.1 + 0.45 = 8.55)

So, any measurement that is between 7.65 ounces and 8.55 will be within 1.5 standard deviations of the mean.

In the given list of measurements, the following meet this requirement:

7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53

So the answer is 11 (E)

Cheers,
Brent