A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The proportion of scores between 300 and 400 is ___.

The proportion of scores between 300 and 400 is 12.03%.

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.

In this problem, we have that:

The proportion of scores between 300 and 400 is

This is the pvalue of Z when X = 400 subtracted by the pvalue of Z when X = 300. So

X = 400

has a pvalue of 0.1335.

X = 300

has a pvalue of 0.0132.

0.1335 - 0.0132 = 0.1203

The proportion of scores between 300 and 400 is 12.03%.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

yes. we do proportions in probabilities.