Question

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?

Answer 1

Suppose a college's SAT scores are normally distributed with mean 1000 and standard deviation 1 for students above 1200. What percentage of students is eligible for scholarships

Answer 2

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

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.