Carcass wrote:
A survey measures the heights of 900 people, which are found to be normally distributed. The mean height is 5′ 5″, and 150 people in the survey have a height between 5′ 1″ and 5′ 3″.
Quantity A |
Quantity B |
The number of people in the survey who are taller than 5′ 9″ |
The number of people in the survey who are more than 2 standard deviations above the mean |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
Points to Remember:1. In a Normally distributed data, 2% of the data lies above and 2% data lies below 2 S.D from mean
2. In a Normally distributed data, 14% of the data lies between 1 and 2 S.D above and 14% of the data lies between 1 and 2 S.D below the mean
3. In a Normally distributed data, 34% of the data lies 1 S.D above and 34% of the data lies 1 S.D below the mean
4. N.D = Mean ± x(S.D), where 0 ≤ x ≤ 3
Now,
Case I: If 5' 9" lies exactly 2 S.D from the mean, then Col. A = Col. B
Case II: If 5' 9" lies less than 2 S.D from the mean, then Col. A > Col. B
Case III: If 5' 9" lies more 2 S.D from the mean, then Col. A < Col. B
For Case I:
5' 9" = 5' 5" + 2(S.D)
2(S.D) = 4 inches
S.D = 2 inches
This means, 5' 1" is 2 S.D below mean; 5' 3" is 1 S.D below mean; and 5' 7" is 1 S.D above mean
Given, 150 people in the survey have a height between 5′ 1″ and 5′ 3″
Therefore, 14% of Data = 150
Data = \(\frac{150}{0.14}\) ≈ 1071 which is far more than 900
This means the S.D of this data is less than 2 inchesSince, S. D < 2 inches, we can say that 5' 9" would lie between 1 S.D and 2 S.D above Mean. So,
Case II is applicableHence, option A
Attachments
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/