A book publisher counted the words on each page of a series of books. They found that the number of words per page followed a normal distribution with a mean of 265 words and a standard deviation of 25 words.

What percentage of the pages contain fewer than 215 words?

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Answer:

The answer is 2.5%

Step-by-step explanation:

Took test on edmentum and made 100%.

2.2% percentage of the pages contain fewer than 215 words.

What is a normal distribution?

The normal distribution is defined as a probability distribution that is symmetric about the mean, indicating that data close to the mean are more systematic in occurrence than data distant from the mean. In pictorial form.

The number of words per page in the book is normally distributed, Normal distribution is given as,
[tex]z = \frac{x-\mu}{\sigma}[/tex]

Where, x = number of words per page., µ = mean, σ = standard deviation
From given, µ = 265 words , σ = 25 words

Probability for the number of pages in the book is less than 265 words,

P( x < 215)
For,  x = 25,
z = (215-265)/25 = -2

From the normal distribution table, the probability of the z score is 0.022


The percent of pages in the book that are less than 215 words in length is 0.022 × 100 = 2.2%.

Thus, 2.2% percentage of the pages contain fewer than 215 words.

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