A total of 150 students have taken an Algebra 2 final exam. The scores are normally distributed with a mean of 71% and standard deviation of 6%. How many students would you expect have scored between 65% and 77%?

Note that 65% and 71% are both 1 standard deviation from the mean (71%). According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students

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Tutorconsortium311 Tutorconsortium311 · Answer 2 · 2022-07-04T16:43:47+02:00

68% of 150 students would be 0.68 (150 students) is, 102 students.

What it means to be normally distributed?

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
In graph form, normal distribution will appear as a bell curve.

What does it mean if your data is not normally distributed?

Collected data might not be normally distributed if it represents simply a subset of the total output a process produced.
This can happen if data is collected and analyzed after sorting.

What are the 4 characteristics of a normal distribution?

Here, we see the four characteristics of a normal distribution.
Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal.
A normal distribution is perfectly symmetrical around its center.

According to the question:

65% and 71% are both 1 standard deviation from the mean (71%).

According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students.

Learn more about normally distributed here:

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