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%