Assume that the test scores from a college admissions test are normally distributed, with a mean of 450 and a standard deviation of 100. a) What percentage of the people taking the test score between 400 and 500

38.3% of the people taking the test score between 400 and 500

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.

In this question, we have that:

What percentage of the people taking the test score between 400 and 500

We have to find the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 400. So

X = 500

has a pvalue of 0.6915

X = 400

has a pvalue of 0.3085

0.6915 - 0.3085 = 0.383

38.3% of the people taking the test score between 400 and 500

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)