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The arithmetic mean and standard deviation for a certain normal distri

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

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New post 12 Feb 2019, 00:50
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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
Spoiler: OA

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Re: The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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New post 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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Re: The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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New post 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
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The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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New post 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.

Answer: E

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

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New post 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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Re: The arithmetic mean and standard deviation for a certain normal distri  [#permalink]

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New post 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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