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 greater than 700. a. 95%.b. 2.5%.c. 5%.d. 97.5%.

b. 2.5%.

Step-by-step explanation:

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

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

Approximately 95% of the measures are within 2 standard deviations of the mean.

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

In this problem, we have that:

Mean of 500, standard deviation of 100.

Percentage of students who scored greater than 700?

700 = 500 + 2*100, so 700 is two standard deviation from the mean.

95% of the scores, are within 2 standard deviations of the mean, so 100 - 95 = 5% are more than 2 standard deviations from the mean. Since the normal distribution is symmetric, 5%/2 = 2.5% will be below 2 standard deviation below the mean(below 300), and 2.5% will be above 2 standard deviation above the mean(above 700). Thus, the correct answer is given by option b.

1 is c

2 is a

3 is a

step-by-step explanation: