Sat scores are normally distributed, with a mean of 1000 and a standard deviation of 200. according to the empirical rule, approximately what percent of the scores will lie between 400 and 1600?

By the Empirical Rule, 99.7% of the scores will lie between 400 and 1600.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 1000

Standard deviation = 200

According to the empirical rule, approximately what percent of the scores will lie between 400 and 1600?

400 = 1000 - 3*200

So 400 is 3 standard deviations below the mean

1600 = 1000 + 3*200

So 1600 is 3 standard deviations above the mean.

By the Empirical Rule, 99.7% of the scores will lie between 400 and 1600.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

-3.5 degrees per hour

step-by-step explanation:

find the unit rate:

-12   1/4 degrees           12.25 degrees

= - = -3.5 degrees per hour

      3   1/2 hours               3.5 hours