Please find the prob in attachment Here i need to know what is meant by "within 1.5 standard deviation of the mean"? [spoiler] OA is E[/spoiler]

I am finding it dificult to read from the picture.Can you please type the question. Also "within 1.5 standard deviation of the mean' means if mean is m the range of the values is m+1.5 to m-1.5

A vending machine is designed to dispense 8 ounces of cofee into a cup.After a test that recorded the number of ounces of coffee in each 1000 cups dispensed by the vending machine ,the 12 listed amounts,in ounces,were selected from the data.IF 1000 recorded amount have a mean of 8.1 ounces and a SD of 0.3 ounce ,how many of the 12 listed amount are within 1.5 SD of the mean? 7.51 8.22 7.86 8.36 8.09 7.83 8.3 8.01 7.73 8.25 7.96 8.53 A)4 B)6 C)9 D)10 E)11

1.5SD = 1.5*0.3 = 0.45 How many of these 12 lie between 8.1 - 0.45 and 8.1 + 0.45, i.e. 7.65 to 8.55 Only 7.51 lies outside these limits. So the answer is 11 out of the 12 are within 1.5 SD

albatross86 wrote:1.5SD = 1.5*0.3 = 0.45 How many of these 12 lie between 8.1 - 0.45 and 8.1 + 0.45, i.e. 7.65 to 8.55 Only 7.51 lies outside these limits. So the answer is 11 out of the 12 are within 1.5 SD Yeah only one data point(7.51) lies outside the range of 7.65 to 8.55. so 11 out of 12 data points reside with in 1.5 SD

The guys above did a great job of explaining. Essentially when the average is plotted on a number line, you can think of standard deviation as the length of a line segment. This will help with translating problems such as: "2 standard deviations above the mean" --> start at the mean and go to the right by two lengths "more than 1.5 standard deviations away from the mean" --> all values that are more than 1.5 lengths away from the mean (both to the right and left) If this problem still gives you any trouble, review its video solution; this is GMATPrep question 1314. You can find similar questions by using the Solutions Engine to search for "standard deviation" Best of luck selango, -Patrick