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?
This question is from the the GMAT Prep Test 1 and 2 so if you haven't worked on those yet go ahead and skip this one for now. It's important to remember that standard deviation is plus or minus. So 1 standard deviation out would be 8.4 on the upper end and 7.8 on the lower end. 1.5 standard deviations out is 8.55 on the upper end and 7.65 on the lower end. Now you just have knock out amounts out of that range. Working backwards is faster since it becomes clear that most of the measurements are falling within 1.5 standard deviations of the mean. Let's also remember that we're not basing all of this on the 8 ounces the vending machine was designed to dispense but on the 8.1 mean that was calculated based on the 1000 cups actually dispensed.