Problem Solving

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 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce,howmany of the 12 listed amounts are written 1.5 standard deviations of the mean?

four
six
nine
ten
eleven

At other forums its multiplying 1.5 and 0.3...please help me clear my concept...why it is to be done to solve this problem

OA:ten

First break up the problem so that you could understand it better.

Given Data,

S.D = 0.3 and Mean = 8.1

They ask as how many are within 1.5 SD of the mean. (Mean is the centric value and 1.5 times SD within the mean would be values on both sides of the number line. i.e lesser or greater than the mean)

So 1.5 times SD = 1.5*0.3 = 0.45.

SO rephrase the question to how many of the above number lie within 8.1 +/- 0.45

or, lie between 7.65 and 8. 55.

Counting from the numbers you get 11. (All expect 7.51)

I guess the answer is 11 to this or maybe you got one of the numbers wrong.