Question

the average number of pages in a novel is 276 witha standard deviation of 18 pages. is a sample of 40 novels is randomly chosen, what is the probability that the average number of pages in these books is between 268 and 281?

Answer 1

$$P(268<X<281)=P(Z<\dfrac{281-276}{18/\sqrt{40}})$$

$$-P(Z\le\dfrac{268-276}{18/\sqrt{40}})$$

$$=P(Z<1.7568)-P(Z\le-2.8109)$$

$$=0.96052-0.00247=0.9581$$