Standard Deviation

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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Sat May 14, 2011 10:16 pm

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 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

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.Four
B.Six
C.Nine
D.Ten
E.Eleven

Can anyone help in solving this? The correct answer is E.

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Source: Beat The GMAT — Problem Solving | Sat May 14, 2011 10:16 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon May 16, 2011 12:43 am

Akansha 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 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

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.Four
B.Six
C.Nine
D.Ten
E.Eleven

Can anyone help in solving this? The correct answer is E.

Solution:
We can apply standard normal distribution in this problem.
Let x stand for the maximum and minimum values that are 1.5 deviations away from the mean which is 8.1.
Also standard deviation is given as 0.3.
So, +1.5 = (x - 8.1)/0.3 and -1.5 = (x - 8.1)/0.3
Or the maximum and minimum values of x are 8.55 and 7.65.
So, number of values in the list which lie in the range 7.65 - 8.55 is 11, the only exception being 7.51.

The correct answer is (E).

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Gurome, Inc.
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