Question

A book editor was proofreading a draft of a novel. She found that the number of errors on each page of the book was normally distributed, with the mean number of errors on a page as 8 and a standard deviation of 1. If 82 pages had between 7 and 9 errors, what was the approximate total number of pages in the book?

Answer 1

Step 1 :

In this question, we are told that :

A book editor was proofreading a draft of a novel.

She found that the number of errors on each page of the book was normally distributed, with the mean number of errors on a page as 8 and a standard deviation of 1.

If 82 pages had between 7 and 9 errors.

We are meant to find the approximate total number of pages in the book.

Step 2 :

`\begin{gathered} \text{Let the total number of pages be x,} \\ Z_9\text{ =}(9-8)/(1)\text{ = 1} \\ Z_{7\text{ }}\text{ = }\frac{7\text{ -8}}{1}\text{ = -1} \end{gathered}`
`\text{Percentage ( Z}_7-Z_9)\text{ = }\frac{68.\text{ 2}}{100}\text{ of x = 82}`
`\begin{gathered} x\text{ =}(82)/(0.682) \\ \text{x = 120.2} \\ x\text{ }\approx\text{ 120 pages} \end{gathered}`

CONCLUSION:

The approximate total number of pages in the book = 120 pages.