1. ## Verbal Scores

The national mean for verbal scores on an exam was 428 and the standard deviation was 113. Approximately what percent of those taking this test had verbal scores between 315 and 541?

2. Originally Posted by magentarita
The national mean for verbal scores on an exam was 428 and the standard deviation was 113. Approximately what percent of those taking this test had verbal scores between 315 and 541?

$(315 < X < 541)$

$(\frac {315-428}{113} < Z < \frac {541-428}{113})$

$(-1 < Z < 1)$

Phi(1) - Phi(-1) = 0.8413-0.1587 = 0.683 = 68.3% is your answer

Also, since it's 1 standard deviation from the mean, we didn't have to calculate it. It's always about 68.3%. 2 SD from the mean is roughly 95%.

3. ## ok.......

Originally Posted by TitaniumX
$(315 < X < 541)$

$(\frac {315-428}{113} < Z < \frac {541-428}{113})$

$(-1 < Z < 1)$

Phi(1) - Phi(-1) = 0.8413-0.1587 = 0.683 = 68.3% is your answer

Also, since it's 1 standard deviation from the mean, we didn't have to calculate it. It's always about 68.3%. 2 SD from the mean is roughly 95%.
Thank you