Standard Deviation Problems 6

[freezer]

• Two different groups of test-takers received scores on the GXYZ standardized test. Group A''s scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B''s scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

a) 1/9
b) 1/8
c) 1/6
d) 4/17
e) 4/21

Thank you very much for a detailed explanation

[krusta80]

• Two different groups of test-takers received scores on the GXYZ standardized test. Group A''s scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B''s scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

a) 1/9
b) 1/8
c) 1/6
d) 4/17
e) 4/21

Thank you very much for a detailed explanation

This requires the use of z-tables I believe. lol

xbar_a = 460
sigma_a = 20

xbar_b = 520
sigma_b = 40

n_a = n_b

P(x_a < 440) = p_a
P(z < (440 - 460)/(sigma_a)) = p_a
P(z < -1) = p_a ~= .1587
p_a = number under 440 / n_a

P(x_b < 440) = p_b
P(z < (440 - 520)/(sigma_b)) = p_b
P(z < -2) = p_b ~= .0228
p_b = number under 440 / n_b

Since n_a = n_b, we can just take the ratio of p_b/(p_a+p_b)

p_b/(p_a+p_b) ~= .0228/(.0228+.1587) ~= .1256 ~= 1/8

B

[lsr]

• Two different groups of test-takers received scores on the GXYZ standardized test. Group A''s scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B''s scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

a) 1/9
b) 1/8
c) 1/6
d) 4/17
e) 4/21

Thank you very much for a detailed explanation

Where did you get that question from?
It's out of Gmat's scope.

[aru4912]

Is there any other approach to solve this question ??

[lsr]

Is there any other approach to solve this question ??

It involves normal distribution (which is outside of GMAT scope)
Looks like a GRE question.....

[aru4912]

hmmm .. interesting !!

[sid007]

In normal distribution curve approx 68% results lie within 1 standard deviation ,95% lie with 2 standard deviation and 99.7(which is approx 100%) lie within 3 standard deviation.
Say x number of folks are present in grp A and B respectively.

Considering this, Grp A folk who score below 440 are the ones who score below 1 standarnd deviation (coz 460-20 =440)
therefore 50-68/2 ie apprx 16% of grp A folks score below 440

Similarly Grp B folks who score below 440 are those who score below 2 standard deviations (coz 520-2*40 = 440)
therefore 50-95/2= approx 2.3% of grp B folks score below 440

so 2.3/(16+2.3) which is approx = 1/8 is the answer.