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. a. 84% b. 16%

b. 16%

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 = 500

Standard deviation = 100

Percentage of students who scored less than 400:

400 = 500 - 1*100

So 400 is one standard deviation below the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those who are below, 68% are within 1 standard deviation of the mean, that is, between 400 and 500. So 100-68 = 32% are below 400.

0.5*0.32 = 0.16 = 16%

So the correct answer is:

b. 16%

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.