Problem Solving

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. 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 SD of the mean? the tewelve listed: 7.51 / 8.22 / 7.86 etc... How we can resolve this ? what is the concept ? I don 't really understand the SD questions ? many thanks

Great word problem. but simple to answer.

trick was to find new SD i.e. 1.5 * .3 = .45

Hi Experts ,

I don't understand the question and the solution, can you please give some other approach. I got this one wrong in my CAT.

Please advise.

Thanks in advance...

I
I
I
I-----------------------------8.55
I
I-----------------------------8.1
I
I----------------------------- 7.65
I
I----------------------------- Zero


All what we need to do is to find the numbers between 8.55 and 7.65.

so the question asked us about how many numbers are within 1.5 SD from the mean.

we know that the mean is 8.1 and we know that the SD is 0.3

so 1.5 of SD is 1.5x 0.3 = 0.45

to find the numbers that are withing this standard deviation is to find all possible numbers that are dispersed from the mean by a maximum of 0.45, meaning that they could be max. away from the mean 0.45 either over the mean or under the mean.

to find numbers which are maximally above the mean by 0.45 , we add 8.1 to 0.45 and then find all the numbers within this range.

then to find the numbers which are maximally below the mean by 0.45 we subtract 0,45 from 8.1 to get 7.65 and look for all numbers within this range.

to simplify all of this, just draw the above figure with m in the middle, m+SD on the top and m-SD on the bottom and find all the numbers that lie within the range of M+SD and M-SD

BINGO!

yass20015 wrote: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. 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 SD of the mean? the tewelve listed: 7.51 / 8.22 / 7.86 etc... How we can resolve this ? what is the concept ? I don 't really understand the SD questions ? many thanks