Answered: The average number of words in a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The average number of words in a romance novel is 64,285 and the standard deviation is 17,145. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible. Please show TI-84 solution

c. The 70th percentile for novels is words. (Round to the nearest word)

d. The middle 40% of romance novels have from words to words. (Round to the nearest word)

Expert Solution

Step 1

The random variable X is defined as the number of words in a randomly selected romance novel which follows normal distribution with mean 64,285 and standard deviation 17,145.

The 70^th percentile for novels is,

$\begin{array}{rcl} P (X < x) & = & 0.70 \\ P (\frac{X - μ}{σ} < \frac{x - 64285}{17145}) & = & 0.70 \\ P (z < \frac{x - 64285}{17145}) & = & 0.70 \end{array}$

The 70^th percentile for novels can be obtained using TI calculator:

Click $2 nd$ button; VARS; and then ‘3’ numbered key to select invNorm(.
Enter 0.70,64285,17145 and close the ‘)’ bracket.
Click Enter.

Output:

From the output, the 70^th percentile for novels is 73,275.8468.

Thus, the 70th percentile for novels is 73,276 words.

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