A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the...

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2554; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon May 25, 2020 5:46 am

Timer

00:00

Answers

Stats

Difficulty—

Source: GMAT Prep

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

The OA is E

Like this post

Source: Beat The GMAT — Problem Solving | Mon May 25, 2020 5:46 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the...

by Brent@GMATPrepNow » Mon May 25, 2020 7:17 am

BTGmoderatorLU wrote: ↑
Mon May 25, 2020 5:46 am
Source: GMAT Prep

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

The OA is E

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

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the...

by Scott@TargetTestPrep » Sat May 30, 2020 1:41 pm

BTGmoderatorLU wrote: ↑
Mon May 25, 2020 5:46 am
Source: GMAT Prep

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

The OA is E

Solution:

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, we see that 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.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review