Answer to Question #187187 in Statistics and Probability for james

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

Solution:

Given, $\mu=326,\sigma=24,n=50$

$X\sim N(\mu,\sigma)$

$P(319\le X\le331)=P(\dfrac{319-326}{24/\sqrt{50}}\le z\le\dfrac{331-326}{24/\sqrt{50}})$

$=P(-0.04\le z\le0.03)=P(z\le0.03)-P(z \le-0.04)$

$=P(z\le0.03)-[1-P(z \le0.04)]=0.51197-[1-0.51595] \\=0.02792$