The median and mode of the students grade is 70.
Most of the students scored between 40 and 100.
Given that,
The mean of the distribution is, μ = 70,
And the standard deviation is, σ = 15
We have to find,
The information about their performances can be obtained by analyzing the curve.
According to the question,
For a Normal distributed data the mean, median and mode are the same.
So, the median and mode of the students grade is 70.
The standard deviation of the data represents the spread of the observation, i.e. how dispersed the values are along the curve.
In statistics, the 68–95–99.7 rule recognized as the empirical rule, is a shortcut used to recall that 68.27%, 95.45% and 99.73% of the values of a Normally distributed data lie within one, two and three standard deviations of the mean, respectively.
[tex]P(\mu-\sigma<x<\mu+\sigma) = P(70-15<x<70+15)= P(55<x<85)= 0.68[/tex]
[tex]P(\mu-2\sigma<x<\mu+2\sigma) = P(70-30<x<70+30)= P(40<x<100)= 0.95[/tex]
[tex]P(\mu-3\sigma<x<\mu+3\sigma) = P(70-45<x<70+45)= P(25<x<115)= 0.997[/tex]
Assuming that maximum marks of the exam is 100, it can be said that most of the students scored between 40 and 100.
For more information about probability click the link given below.
https://brainly.com/question/2773823
