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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 57 inches, and standard deviation of 7.3 inches.What is the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

In the country of United States of Heightlandia the height measurements of tenyearold children are approximately normally distributed with a mean of 57 inches a class=

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Answer:

0.834

Explanations:

The formula calculating the z-score is expressed as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Given the following parameters

• x1 = 49.55

,

• x2 = 73.35

,

• mean μ = 57inches

,

• standard deviation σ = 7.3in

Convert the x-values to z-score

[tex]\begin{gathered} z_1=\frac{x_1-\mu}{\sigma} \\ z_1=\frac{49.55-57}{7.3} \\ z_1=-\frac{7.45}{7.3} \\ z_1=-1.02 \end{gathered}[/tex]

For z2;

[tex]\begin{gathered} z_2=\frac{73.35-57}{7.3} \\ z_2=\frac{16.35}{7.3} \\ z_2=2.24 \end{gathered}[/tex]

Determine the required probability

[tex]\begin{gathered} P(-1.02Hence the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches is 0.834

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