Question

1. Suppose that the scores on a national achievement exam have a mean of 480 and a standard deviation of 90. If the scores are normally distributed, then find the range for which 68%, 95%, and 99.7% of the scores will fall between.

Answer 1

Approximately 68% data falls between 1 standard deviation of the mean

That is between

Mean - SD and Mean + SD

480 - 90 and 480 + 90

390 and 570

Approximately 95% data falls between 2 standard deviation of the mean

That is between

Mean - 2 * SD and Mean + 2* SD

480 - 2 * 90 and 480 + 2 * 90

300 and 660

Approximately 99.7% data falls between 3 standard deviation of the mean

That is between

Mean - 3 * SD and Mean + 3 * SD

480 - 3 * 90 and 480 + 3 * 90

210 and 750