Answer to Question #218619 in Statistics and Probability for Andrea

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

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