Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 13:54 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A vending machine is designed to dispense 8 ounces of coffee

Author Message
TAGS:

### Hide Tags

Intern  Joined: 06 Oct 2017
Posts: 1
A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

### Show Tags

Here's another way to solve this problem by NOT multiplying values:

I did it by dividing 1,5/2= 0,75 in each direction (8,1 +/- 0,75), then substract 0,3 from 0,75 (+/- 0,75), so you get 0,45. Then, of the 12 amounts listed, 11 are within the range of 8,1 - 0,45 or 8,1 + 0,45.
Intern  B
Joined: 26 Dec 2016
Posts: 29
Re: A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

### Show Tags

Bunuel wrote:
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?

A. four
b. Six
c. Nine
d. Ten
e. Eleven

I tried to explain this here: https://gmatclub.com/forum/a-vending-ma ... ml#p812247

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.
[/quote][/quote]

I'm sorry, but this still doesn't make sense to me why you multiplied the standard deviations. With SD=0.3 then 1 deviation away would be 8.4 and with SD=1.5 it'd be 9.6. Where does the reasoning for multiplying both SD come from?
CEO  V
Joined: 12 Sep 2015
Posts: 3851
Re: A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

### Show Tags

Top Contributor
zz0vlb wrote:
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?

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

If the Standard Deviation is 0.3 ounces, then 0.3 ounces represents 1 unit of standard deviation.
Similarly, 0.6 ounces represents 2 units of standard deviation,
0.15 ounces represents 0.5 units of standard deviation, and so on.

If the mean is 8.1 ounces, then we say that 8.4 ounces is 1 unit of standard deviation above the mean (since 8.1 + 0.3 = 8.4), and we say that 7.8 ounces is 1 unit of standard deviation below the mean (since 8.1 - 0.3 = 7.8)

We want to know how many measurements in the list are within 1.5 standard deviations of the mean

Well, using the above logic, 0.45 represents 1.5 units of standard deviation.

So, 1.5 units of standard deviation below the mean equals 7.65 (8.1 - 0.45 = 7.65)
Similarly, 1.5 units of standard deviation abovethe mean equals 8.55 (8.1 + 0.45 = 8.55)

So, any measurement that is between 7.65 ounces and 8.55 will be within 1.5 standard deviations of the mean.

In the given list of measurements, the following meet this requirement:

7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53

So the answer is 11 (E)

Cheers,
Brent
_________________
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822
Re: A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

### Show Tags

zz0vlb wrote:
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?

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

We are given 12 listed amounts of coffee that we can put in order from least to greatest.

7.51, 7.73, 7.83, 7.86, 7.96, 8.01, 8.09, 8.22, 8.25, 8.30, 8.36, 8.53

We need to determine how many of the listed amounts are within 1.5 standard deviations of the mean. Since the standard deviation is 0.3, 1.5 standard deviations is: 1.5 x 0.3 = 0.45.

1.5 standard deviations above the mean is 8.1 + 0.45 = 8.55

1.5 standard deviations below the mean is 8.1 – 0.45 = 7.65

We see that all the values are between 7.65 and 8.55 except 7.51. Thus, 11 values are within 1.5 standard deviation of the mean.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A vending machine is designed to dispense 8 ounces of coffee   [#permalink] 30 Aug 2018, 17:49

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by

# A vending machine is designed to dispense 8 ounces of coffee  