Question

Comparing SAT and ACT: Suppose that the distribution of scores on the SAT exam is approx. normal with a mean of 1000 and a standard deviation of 160, while the distribution of scores on the ACT exam is approx. normal with a mean of 21 and a standard deviation of 5. Approx 95% of ACT scores fall between two values. What is the value of the lower value

Answer 1

11

Explanation:

According to the empirical rule, 95% of data in a normal distribution will be between 2 standard deviations below the mean and 2 standard deviations above the mean.

Therefore, 2 standard deviations above the mean would be 21+2(5)=21+10=31 and 2 standard deviations below the mean would be 21-2(5)=21-10=11.

Thus, the lower value is 11