## A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. L

Question

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Let X=, the height of a randomly selected student from this set.

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2022-02-13T21:44:19+00:00
2022-02-13T21:44:19+00:00 2 Answers
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## Answers ( )

Answer:0.11

Step-by-step explanation:This is the answer for the Kahn Academy, not sure why the other was so off

Answer:The proportion of students whose height are lower than Darnell’s height is 71.57%

Step-by-step explanation:The complete question is:

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnel is a middle school student with a height of 161.4cm.

What proportion of proportion of students height are lower than Darnell’s height.

Answer:

We first calculate the z-score corresponding to Darnell’s height using:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

We substitute x=161.4 , [tex]\mu=150[/tex], and [tex]\sigma=20[/tex] to get:

[tex]Z=\frac{161.4-150}{20} \\Z=0.57[/tex]

From the normal distribution table, we read 0.5 under 7.

The corresponding area is 0.7157

Therefore the proportion of students whose height are lower than Darnell’s height is 71.57%