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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 53.2 inches, and standard deviation of 3 inches.What is the probability that the height of a randomly chosen child is between 49.8 and 60.6 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

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EXPLANATION

Given that the mean is 53.2 inches, and standard deviation of 3 inches. We will first find the z scores for height 49.8 and 60.6. inches

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z_{49.8}=\frac{49.8-53.2}{3}=-1.13333 \\ z_{60.6}=\frac{60.6-53.2}{3}=2.46667 \end{gathered}[/tex]

Therefore,

Using a z score calculator, The probability that the height of a randomly chosen child is between 49.8 and 60.6 inches is

[tex]P\left(49.8Answer: 0.865

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