Lisa has collected data to find the number of pages per book shelf has normal distribution what is probability that a randomly selectedcbiok hascfewer than 135 pages if mean is 191 pages and standard deviation is 28 pages

P(X<135)=0.0228

Step-by-step explanation:

The data Lisa collected to find the number of pages per book shelf has normal distribution with mean 191 pages and standard deviation is 28 pages

We first find the z-score using:

We substitute

We read from the standard normal distribution table -2 under 0 to obtain:

P(X<135)=0.0228

The probability that a randomly selected book has fewer than 135 pages is 0.02275

Step-by-step explanation:

To find the probability of random variable X which has a normal distribution we use the z-score

The formula of z-score is z = (X - μ)/σ , where

∵ The mean is 191 pages

∴ μ = 191

∵ The standard deviation is 28 pages

∴ σ = 28

∵ The book has fewer than 135 pages

∴ X = 135

- Substitute all of these numbers in the formula of z-score

∴ z-score =

∴ z-score = -2

Use the normal distribution table of z to find the corresponding area of the z-score

∵ The corresponding area of z = -2 is 0.02275

- The probability is the area to the left of z-score

∴ P(X < 135) = 0.02275

The probability that a randomly selected book has fewer than 135 pages is 0.02275

21

step-by-step explanation:

the answer is 21%.