Respuesta :
Answer:
Mean is 76 and standard deviation is 7.
Step-by-step explanation:
Let [tex]\mu[/tex] be the mean and [tex]\sigma[/tex] is the standard deviation of the given data,
Thus, 95% of the data lies between [tex]\mu-2\sigma[/tex] and [tex]\mu+2\sigma[/tex]
Now, 95% of students at school weigh between 62 kg and 90 kg,
So, the mean is,
[tex]\mu=\frac{62+90}{2}=\frac{152}{2}=76[/tex]
[tex]\implies 76+2\sigma = 90[/tex]
[tex]2\sigma = 14[/tex]
[tex]\implies \sigma = 7[/tex]
Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the given data is 76 and the standard deviation of the given data is 7.
What is mean and standard deviation of normally distributed data?
Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data.
The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
Given information-
Total percentage of the students at school weight between 62-90 kg is 95 percent.
Data is normally distributed.
The mean of the given data is,
[tex]\mu=\dfrac{62+90}{2} \\\mu=76[/tex]
Thus the mean of the given data is 76.
The standard deviation of the given data is,
[tex]\sigma=\dfrac{90-76}{2} \\\sigma=7[/tex]
Thus the standard deviation of the given data is 7.
Hence the mean of the given data is 76 and the standard deviation of the given data is 7.
Learn more about the normally distributed data here;
https://brainly.com/question/6587992
