Question

Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 140 pages if the mean is 194 pages and the standard deviation is 27 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.

I can get to the Z value, but I dont know how to solve P(Xbar<140). Thank you so much!

Answer 1

Mean = = 194

SD = = 27

To find P(X<140):

Z = (140 - 194)/27

= - 2.00

By Empirical Rule:

95% of the data falls within 2 standard deviations of the mean.

So,

Probability of data points from mid value to 2 standard deviations on LHS = 0.95/2 = 0.475

So,

Probability of data points less than 2 standard deviations on LHS = 0.50 - 0.475 = 0.025

So,

The probability that a randomly selected book has fewer than 140 pages if the mean is 194 pages and the standard deviation is 27 pages =0.0250 = 2.50 %

So,

Answer is:

2.50 %