The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400.

The percentage of students who scored less than 400 is 16%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) 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:

Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400.

400 = 500 - 100

So 400 is one standard deviation below the mean.

By the Empirical Rule, 68% of the students scored within 1 standard deviation of the mean, that is, within 400 and 600. The other 32% scores were more than 1 standard deviation from the mean. Since the normal distribution is symmetric, 16% scored more than one standard deviation below the mean(less than 400) and 16% scored more than one standard deviation above the mean(more than 600). So

The percentage of students who scored less than 400 is 16%.

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