Answer to Question #202055 in Statistics and Probability for kim

Question

The average number of pages in a novel is 326 with a standard deviation of 24

pages. If a sample of 50 novels is randomly chosen, what is the probability that

the average number of pages in these books is between 319 and 331?

Answer 1

$\mu=326 \\ \sigma=24 \\ n=50 \\ P(319< \bar{X}<331) = P(\bar{X}<331) -P(\bar{X}<319) \\ = P(Z <\frac{331-326}{24/ \sqrt{50}}) -P(Z< \frac{319-326}{24 / \sqrt{50}}) \\ = P(Z< 1.473) -P(Z< -2.062) \\ = 0.9296 -0.0196 \\ = 0.91$