Vending Machine - Std Dev

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Fri Jan 06, 2012 8:32 pm

A vending m/c is designed to dispense 8 ounces of coffee per cup. After a test that recorded no of ounces of coffee in each of the 1000 cups dispensed by the vending m/c, the 12 listed amounts, in ounces, were selected for the data. if the 1000 recorded data have a mean of 8.1 ounces and standard deviation of 0.3, how many of the 12 listed amounts comes within 1.5 std dev of the mean?

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

Four
Six
Nine
Ten
Eleven

Last edited by karthikpandian19 on Fri Jan 06, 2012 8:49 pm, edited 1 time in total.

Source: Beat The GMAT — Problem Solving | Fri Jan 06, 2012 8:32 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 » Fri Jan 06, 2012 8:36 pm

karthikpandian19 wrote:A vending m/c is designed to dispense 8 ounces of coffee per cup. After a test that recorded no of ounces of coffee in each of the 1000 cups dispensed by the vending m/c, the 12 listed amounts, in ounces, were selected for the data. if the 1000 recorded data have a mean of 8.1 ounces and standard deviation of 0.3, how many of the 12 listed amounts comes within 1.5 std dev of the mean?

Four
Six
Nine
Ten
Eleven

What are the 12 listed amounts?

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Fri Jan 06, 2012 8:47 pm

sorry abt tht...adding now...

Anurag@Gurome wrote:
karthikpandian19 wrote:A vending m/c is designed to dispense 8 ounces of coffee per cup. After a test that recorded no of ounces of coffee in each of the 1000 cups dispensed by the vending m/c, the 12 listed amounts, in ounces, were selected for the data. if the 1000 recorded data have a mean of 8.1 ounces and standard deviation of 0.3, how many of the 12 listed amounts comes within 1.5 std dev of the mean?

Four
Six
Nine
Ten
Eleven
What are the 12 listed amounts?

GMAT/MBA Expert

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 » Fri Jan 06, 2012 8:53 pm

karthikpandian19 wrote:sorry abt tht...adding now...

S.D. = 0.3 implies 1.5 S.D. = 0.3 * 1.5 = 0.45
Mean = 8.1
"Within 1.5 standard deviation of the mean" means mean in the range 8.1 – 0.45 and 8.1 + 0.45, which means in the range 7.65 and 8.55
From the 12 listed amounts only 7.51 is not in the range, which means 11 amounts are within the range.

The correct answer is E.

karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Fri Jan 06, 2012 8:59 pm

I didnt understand:

S.D. = 0.3 implies 1.5 S.D. = 0.3 * 1.5 = 0.45

Anurag@Gurome wrote:
karthikpandian19 wrote:sorry abt tht...adding now...
S.D. = 0.3 implies 1.5 S.D. = 0.3 * 1.5 = 0.45
Mean = 8.1
"Within 1.5 standard deviation of the mean" means mean in the range 8.1 – 0.45 and 8.1 + 0.45, which means in the range 7.65 and 8.55
From the 12 listed amounts only 7.51 is not in the range, which means 11 amounts are within the range.

The correct answer is E.

GMAT/MBA Expert

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 » Fri Jan 06, 2012 9:06 pm

karthikpandian19 wrote:I didnt understand:

S.D. = 0.3 implies 1.5 S.D. = 0.3 * 1.5 = 0.45

It's given that standard deviation = 0.3, so 1.5 * standard deviation means 1.5 * 0.3 = 0.45

karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Fri Jan 06, 2012 9:08 pm

Oh...Ok

I assumed / interpreted that the SD to be 1.5......

Anurag@Gurome wrote:
karthikpandian19 wrote:I didnt understand:

S.D. = 0.3 implies 1.5 S.D. = 0.3 * 1.5 = 0.45

It's given that standard deviation = 0.3, so 1.5 * standard deviation means 1.5 * 0.3 = 0.45

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