Answer:
Step-by-step explanation:
Assuming a normal distribution for the distribution of the points scored by students in the exam, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = points scored by students
u = mean score
s = standard deviation
From the information given,
u = 70 points
s = 10.
We want to find the probability of students scored between 40 points and 100 points. It is expressed as
P(40 lesser than x lesser than or equal to 100)
For x = 40,
z = (40 - 70)/10 =-3.0
Looking at the normal distribution table, the corresponding z score is 0.0135
For x = 100,
z = (100 - 70)/10 =3.0
Looking at the normal distribution table, the corresponding z score is 0.99865
P(40 lesser than x lesser than or equal to 100) = 0.99865 - 0.0135 = 0.98515
The percentage of students scored between 40 points and 100 points will be 0.986 × 100 = 98.4%
In this exercise we have to use the knowledge of statistics to calculate the probability value, so we have to:
98.4%
Knowing that the distribution formula is given by:
[tex]z = (x - u)/s[/tex]
Where
So the probability will be:
[tex]z = (40 - 70)/10 =-3.0\\z = (100 - 70)/10 =3.0[/tex]
Making the difference we have:
[tex]P = 0.99865 - 0.0135 = 0.98515 = 98.4\%[/tex]
See more about statistics at brainly.com/question/10951564
