Chapter 6 - Section 6.5 - The Normal Approximation to the Binomial Distribution - Exercises - Page 262: 6.46

a. n = 25, p = .40 $P(8\leq x \leq 13)$ = 0.12+0.1511+0.1612+0.1465+0.1140+0.076=0.7688 b. mean = np = 25*.4 = 10 , standard deviation = $\sqrt (npq) $ =$\sqrt (25*.40*.60) $ = 2.4495 $P(8\leq x \leq 13)$ = $P(\frac{8-10}{2.4495}\leq z \leq \frac{13-10}{2.4495})$ = $P (-0.8165 \leq z \leq 1.2247)$ = .6826 Difference between the approximations = 0.7688-0.6826 = 0.0862

See above.