Answer to Question #127772 in Statistics and Probability for Jack

Question

The thickness of books in a bookstore follows a normal distribution with the mean of 45mm and the standard
deviation of 12mm.
a) A book is obtained from the bookstore, find the probability that
i) The book is thinner than 30mm.
ii) The book’s thickness is between 34mm and 50mm.
b) 10 books are chosen from the bookstore at random, the mean thickness of that 10 books,

Answer 1

i) P(x<30)

z=(30-45)/12=-1.25

using table, P(x<30)=0.10565

ii) P(34<x<50)=P(x<50)-P(x<34)

P(x<50)

z=(50-45)/12=0.42

using table, P(x<50)=0.66276

P(x<34)

z=(34-45)/12=-0.92

using table, P(x<34)=0.17879

P(34<x<50)=0.66276-0.17879=0.48397

b) mean thikness x=$\mu=45$