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I've been working on this problem and I just can't seem to come up with the right answer.

The question goes:

Consider a normal distribution curve where 60-th percentile is at 11 and the 25-th percentile is at 9. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

I found the mean to be 10.44680851 which is right. But the problem is I just can't seem to find the right answer for standard deviation.

Here is how I tried to solve the problem,

Since the probability of X = 9 is 0.25 (25th percentile) and X = 11 is 0.6(60th percentile), I found Z-values that correspond with those probabilities and came up with two equations:

μ + (-0.68)σ = 9

μ + 0.26σ = 11

When I solved the equation the answer comes out to be 2.12765.. but apparently that's not the right answer!

Any idea? Thx in advance~

Cheul Hee Jason Yoo
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  • Surely you do not mean to say that $\mu $ plus a negative quantity, namely $-0.26$ times $\sigma$, is $11$, The $60$-th percentile is above the mean. That equation should be roughly $\mu+0.26\sigma=11$, I checked. I did not check your other equation, but there negative is right. – André Nicolas Oct 25 '15 at 00:13
  • yes, you are right. There was a mistake. Sharp eyes~ – Cheul Hee Jason Yoo Oct 25 '15 at 00:17

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