Problem Solving

If 96 percent of women 25-59 years of age at Country Q weigh between 97.5 lbs and 155 lbs, and this data is normally distributed, then which of the following is the best approximation for the mean and standard deviation of their weights in pounds, respectively?
A. 100 and 30
B. 110 and 25
C. 120, and 20
D. 125 and 15
E. 140, and 10


Made Up!

sanju09 wrote:If 96 percent of women 25-59 years of age at Country Q weigh between 97.5 lbs and 155 lbs, and this data is normally distributed, then which of the following is the best approximation for the mean and standard deviation of their weights in pounds, respectively?
A. 100 and 30
B. 110 and 25
C. 120, and 20
D. 125 and 15
E. 140, and 10


Made Up!

Sanju09,

Is Answer D ?

Regards,
Uva.

Tough GMAT problems expect us know the answers of any of the following questions:

"¢ What is Standard Deviation?
"¢ How is Standard Deviation related with Variance and Range of a distribution?
"¢ What is the significance of Standard Deviation?
"¢ What is Normal Distribution, and what is it to do with the Standard Deviation and the Bell Curve?
"¢ What is a Bell Curve? What is the approximated break up percentages of the Bell Curve?
"¢ What do we mean by 1 or 2 Standard Deviation(s) below or above the Mean? Etc...

Yes, GMAT never make us calculate the Standard Deviation the real way, but at the same time it may test us over the understanding, applying, and approximating the Standard Deviation from the necessary info provided.

96 percent is almost 100 percent. If this data is normally distributed, then 97.5 lbs and 155 lbs are the real extremes, whose average is the approximated mean.

� Mean = (97.5 + 155)/2, approximately equal to 125.

If 97.5 lbs and 155 lbs are the real extremes, then the Range of the distribution is the difference of the extremes.

� Range = 155 - 97.5, or approximately equal to 57; and in the absence of real data, if only the Range of the data is known, one-fourth of the Range is an rough approximation for the Standard Deviation. Hence, the Standard Deviation of the presented data is roughly around ¼ (57), 15 is the best value to pick.

[spoiler]Where do we find 125 and 15 together?[/spoiler]

Uva@90 wrote:

sanju09 wrote:If 96 percent of women 25-59 years of age at Country Q weigh between 97.5 lbs and 155 lbs, and this data is normally distributed, then which of the following is the best approximation for the mean and standard deviation of their weights in pounds, respectively?
A. 100 and 30
B. 110 and 25
C. 120, and 20
D. 125 and 15
E. 140, and 10


Made Up!

Sanju09,

Is Answer D ?

Regards,
Uva.

Have you lost it like him? The GMAT never asks questions about Normal Distribution!

Surely the mean would just be symmetrically between the 97.5 and 155 poles (with 2% either side of that again)? 126.25

Answer D?

Correction

if only the Range of the data is known, one-fourth of the Range is a rough approximation for the Standard Deviation.

Can anybody tell what I really corrected?
A. He
B. Will
C. Get
D. An
E. Apple

[spoiler]PS: Brent is absolutely correct that the OG never used the term Normal Distribution. Fault is mine, because when I describe SD in a GMAT session, I prefer to provide them the mystery from all weird corners. I request the esteemed moderators to move this thread to some GRE bin and wash hands.[/spoiler]