Can you please understand how to go about these problems?
1) 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 coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 amounts are within 15 standard deviations of the mean?

Answer:11
WHY?

2) Three grades of milk are 1%, 2%, 3% fat by volume. If x gallons of 1% grade, y gallons of 2% grade, z gallons of 3 % grade are mixed to give x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

Answer: y+3z
WHY?

Please provide the Veritas text, page, and problem number. Or if the problems are from exams provided by Veritas, please provide (or email to help@veritasprep.com) screen copies.

Thanks.

- Veritas Help

Hi, hmmm this is a tricky problem! Not sure why the answer is either...because after apply 15 of the standard deviations, it yields a range of 3.60 - 12.60, which all of the 12 samples seem to fall under...

@VeritasHelp: Any insight into this?

As for the "grades of milk problem", here's how I went about it:

First translate the prompt into algebra:
x(0.01) * Y(0.02) * Z(0.03) = (x+y+z)(0.015)
Then distribute the (0.015) on the right-hand side:
x(0.01) * Y(0.02) * Z(0.03) = x(0.015) + y(0.015) + z(0.015)
Then just combine like terms and isolate the x on one side, this will eventually yield the answer equation of:
x = y + 3z

Hey Derek,

Good question - and you're right as the problem is written. But as the original question is written, it's 1.5 standard deviations (and not 15...I don't think many statistical sample sets go to 15 standard deviations!), so that's why the range is from 0.45 on either side of the mean, and only 11 of the 12 values fit.

Great! Phew! Thought I was missing something KEY there. Thanks Brian!