Question

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.

Answer 1

0.834

Explanations:

The formula calculating the z-score is expressed as:

`z=(x-\mu)/(\sigma)`

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

`\begin{gathered} z_1=(x_1-\mu)/(\sigma) \\ z_1=(49.55-57)/(7.3) \\ z_1=-(7.45)/(7.3) \\ z_1=-1.02 \end{gathered}`

For z2;

`\begin{gathered} z_2=(73.35-57)/(7.3) \\ z_2=(16.35)/(7.3) \\ z_2=2.24 \end{gathered}`

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