Suppose SAT Critical Reading scores are normally distributed with a mean of 501 and a standard deviation of 110. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission

The minimum score required for admission is 558.75.

Step-by-step explanation:

When the distribution is normal, we use 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.

Suppose SAT Critical Reading scores are normally distributed with a mean of 501 and a standard deviation of 110.

This means that

A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission

This is the 100 - 30 = 70th percentile, which is X when Z has a pvalue of 0.7. So X when Z = 0.525. So

The minimum score required for admission is 558.75.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584