Question

Consider a normal distribution curve where 80-th percentile is at 19 and the 20-th percentile is at 1. Use this information to find the mean, ? μ , and the standard deviation, ? σ , of the distribution.  Note: this is a tricky problem, you should get out a pen and paper and work through it carefully.

Answer 1

Using z percentile table, we get z = -0.84 and z = 0.84 for 20th percentile and 80th percentile respectively.

Using z score formula, we can write

and

Adding both these equations, we get

And setting mean (mu) = 10 in first equation, we get

Therefore, mean is 10 and standard deviation is 10.71

If we use 80th percentile = 0.842 and 20th percentile = -0.842, then standard deviation will change

standard deviation = (19-10)/0.842 = 10.69