* do-file for Supplementary Exercise 5.59 of IPS7e
version 13 /* works also with version 14 */

* binomial distribution
* P(463<=X<=523) = P(X<=523) - P(X<=462)
display binomial(1006,523,.49)
display binomial(1006,462,.49)
display binomial(1006,523,.49) - binomial(1006,462,.49)

* normal approximation of binomial probability
display normal((523+0.5-1006*.49)/sqrt(1006*.49*.51)) - normal((463-0.5-1006*.49)/sqrt(1006*.49*.51))

* direct normal approximation of distribution of p_hat
display normal((0.52-0.49)/sqrt(.49*.51/1006)) - normal((0.46-0.49)/sqrt(.49*.51/1006))