Respuesta :
Answer:
The boy was above average by 3 SDs.
i.e. 3*SD=3*8=24 cm above the average value.
Step-by-step explanation:
Given:
3015 boys with age of 11 ,Avg height of 146 cm and Standard deviation of 8 cm.
To find:
How above Avg 170 cm tall boy is?
Solution:
The mean of 3015 boys is of 146 cm in height,
And standard deviation is 8cm.
the height of one boy is 170 cm ,
This boy's height is 24 cm above the average height.
i.e. 170 cm -146cm=24 cm.
Hence , standard deviation is of 8cm .
1 SD=8cm
2SD=8+8=16 cm
3SD= 8+8+8=24 cm.
The height of boy in compare of standard deviation=24/8 .
=3
Hence the height of the boy 3 times the standard deviation ,170cm.
Using the normal distribution, it is found that:
- He was above average by 3 SDs.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
In this problem:
- The average height is of 146 cm, hence [tex]\mu = 146[/tex].
- The standard deviation is of 8 cm, hence [tex]\sigma = 8[/tex].
- The boy was 170 cm tall, hence [tex]X = 170[/tex].
Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{170 - 146}{8}[/tex]
[tex]Z = 3[/tex]
He was above average by 3 SDs.
To learn more about the normal distribution, you can take a look at https://brainly.com/question/24663213
