Question

Find the percentage of scores in between a score of 120 and a score of 140 with a mean of 136 and standard devaition of 12

Answer 1

By the Central Limit Theoreme

$$\frac {x - E X}{\sqrt {D X}} \sim x \sim N (0, 1)$$

So

$$P (1 2 0 < x < 1 4 0) = P \left(\frac {1 2 0 - 1 3 6}{1 2} < \frac {x - 1 3 6}{1 2} < \frac {1 4 0 - 1 3 6}{1 2}\right) =$$ $$P (- 1. 1 6 < \frac {x - 1 3 6}{1 2} < 0. 5) = F (0. 5) - F (- 1. 1 6) = 5 7 \%$$