Question

SAT scores were originally scaled so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Use the empirical rule to estimate the probability that a randomly selected student gets with a section score of 700 or better.

a. 2.5%
b. 95%
c. 5%
d. 97.5%​

Answer 1

a. 2.5%

Explanation:

The Z-score of the given test score is ...

Z = (X -μ)/σ = (700 -500)/100 = 2

The empirical rule tells you 95% of a normal distribution is within 2σ of the mean. The other 5% is split evenly between the two tails of the distribution, so the probability of a score 2σ or more above the mean is about 1/2×5% = 2.5%.