Question

The number of words per page in a certain book is normally distributed with a mean of 340 words and a standard deviation of 20 words.

Approximately what percent of pages in the book are less than 360 words in length?

Answer 1

Explanation:

Since the number of words per page in the book is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = number of words per page.

µ = mean

σ = standard deviation

From the information given,

µ = 340 words

σ = 20 words

The probability that the number of pages in the book are less than 360 words in length is expressed as

P(x < 360)

For x = 360,

z = (360 - 340)/20 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

The percent of pages in the book that are less than 360 words in length is

0.84 × 100 = 84%