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# The arithmetic mean and standard deviation for a certain normal distri

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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12 Feb 2019, 00:50
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:14) correct 33% (01:30) wrong based on 33 sessions

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The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respectively. Which of these values is more than 2.5 standard deviations from the mean?

(A) 5.75
(B) 6
(C) 6.5
(D) 13.25
(E) 13.5

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
Re: The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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12 Feb 2019, 00:51
Bunuel wrote:
The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respectively. Which of these values is more than 2.5 standard deviations from the mean?

(A) 5.75
(B) 6
(C) 6.5
(D) 13.25
(E) 13.5

Similar question from OG: https://gmatclub.com/forum/the-arithmet ... 29117.html
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Joined: 11 Dec 2018
Posts: 10
Re: The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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12 Feb 2019, 02:48
Bunuel wrote:
The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respectively. Which of these values is more than 2.5 standard deviations from the mean?

(A) 5.75
(B) 6
(C) 6.5
(D) 13.25
(E) 13.5

IMHO E is te correct answers!

9.5 = mean
1.5= sd

1.5*2.5= 3.75

x > 9.5 +3,75
x > 13.25
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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Updated on: 13 Feb 2019, 22:35

Solution

Given:
• The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respectively.

To find:
• Among the given options, which one is more than 2.5 standard deviations from the mean.

Approach and Working:
• As the standard deviation is 1.5, the value of 2.5 standard deviations = 2.5 x 1.5 = 3.75
• 3.75 more than the mean = 9.5 + 3.75 = 13.25

Therefore, the value more than 13.25 present in the options is 13.5

Hence, the correct answer is option E.

_________________

Originally posted by EgmatQuantExpert on 12 Feb 2019, 03:09.
Last edited by EgmatQuantExpert on 13 Feb 2019, 22:35, edited 1 time in total.
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Joined: 18 Aug 2017
Posts: 4999
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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12 Feb 2019, 05:18
Bunuel wrote:
The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respectively. Which of these values is more than 2.5 standard deviations from the mean?

(A) 5.75
(B) 6
(C) 6.5
(D) 13.25
(E) 13.5

value = mean + sd * 2.5

value = 9.5+ 2.5*1.5
= 13.25

vlaue more than 13.25 given is 13.5

IMO E
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Joined: 09 Mar 2018
Posts: 996
Location: India
Re: The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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12 Feb 2019, 05:27
Bunuel wrote:
The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respectively. Which of these values is more than 2.5 standard deviations from the mean?

(A) 5.75
(B) 6
(C) 6.5
(D) 13.25
(E) 13.5

2.5 SD from the mean = 13.25

9.5 + 1.5 * 2 + 1.5 *0.5 = 13.25

Only E is more than 13.25
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Re: The arithmetic mean and standard deviation for a certain normal distri   [#permalink] 12 Feb 2019, 05:27
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