SOLUTION: Consider a normal distribution curve where 90-th percentile is at 14 and the 45-th percentile is at 6. Use this information to find the mean, μ , and the standard deviation, σ ,

Question 1179579: Consider a normal distribution curve where 90-th percentile is at 14 and the 45-th percentile is at 6. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.
a) μ=

b) σ=
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

(1) Use a z-score table or any other reference to determine that the 45th percentile is 0.125 standard deviations below the mean and the 90th percentile is 1.282 standard deviations above the mean.

(2) Determine the standard deviation knowing that the difference between the 45th and 90th percentiles is 0.125+1.282=1.407 standard deviations, and the difference between the values at those percentiles is 14-6=8.

(3) Determine the mean, knowing that it is 0.125 standard deviations above the 45th percentile, or knowing that it is 1.282 standard deviations below the 90th percentile. To check your calculations, verify that both calculations give you the same value for the mean.

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