Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Middle 85%

Goes from X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to X when Z has a pvalue 0.5 + 0.85/2 = 0.925.

Lower limit is 8

This means that when X = 8, Z has a pvalue of 0.075. So when .

Upper limit is 14

This means that when X = 14, Z has a pvalue of 0.925. So when .

From the lower limit, we have that

So

And

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step-by-step explanation:

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