In the country of United States of Heightlandia, the height measurements of ten-year-old children areapproximately normally distributed with a mean of 56.2 inches, and standard deviation of 3.5 inches,What is the probability that the height of a randomly chosen child is between 53.05 and 58.65 inches? Donot round until you get your your final answer, and then round to 3 decimal places.Answer=(Round your answer to 3 decimal places.)

Answered: In the country of United States of…

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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In the country of United States of Heightlandia, the height measurements of ten-year-old children are
approximately normally distributed with a mean of 56.2 inches, and standard deviation of 3.5 inches,
What is the probability that the height of a randomly chosen child is between 53.05 and 58.65 inches? Do
not round until you get your your final answer, and then round to 3 decimal places.
Answer=
(Round your answer to 3 decimal places.)

Expert Solution

Step 1

The probability that the height of a randomly chosen child is between 53.05 and 58.65 inches is calculated as below:

$\begin{array}{rcl} P (53.05 & < & x < 58.65) = P (\frac{x - 56.2}{3.5} < z < \frac{x - 56.2}{3.5}) \\ = & P (\frac{53.05 - 56.2}{3.5} < z < \frac{58.65 - 56.2}{3.5}) \\ = & P (- 0.9 < z < 0.7) \\ = & P (z < 0.7) - P (z < - 0.9) \end{array}$

The p value is obtained using excel function "=NORMSDIST(z)"

output obtained using excel is below:

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