Ezra scores 680 on the mathematics portion of the sat. the distribution of sat math scores in recent years has been normal with a mean of 518 and a standard deviation of 114. what is the z-score for ezra's sat math score?

The z-score is given by:



where z is the z-score, x is the value whose z-score we want to calculate, μ is the mean, and σ is the standard deviation.

Hence, in your example:



The z-score of a value is the number of standard-deviations the value is above the mean. In this case, Ezra's score is 1.42 standard-deviations above the mean.

This standardized value allows you to answer questions like: "Is Ezra's score a high score?" Well, it's obviously above the mean (162 points above the mean). But, is that a high difference? With the z-score you know that it is 1.42 standard-deviations above the mean. In a normal distribution, only 16% of the values are 1 standard deviation or more above the mean, and only 2.3% are above 2 standard deviations or more above the mean. Hence, Ezra's is a high score (between the 16% and the 2.3% best scores).

Ibelieve it is

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.