The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 65 points. About what percent of students have scored between 60 and 65 points?

34%

Step-by-step explanation:

Since the points obtained by students of the class in a test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = points obtained by students

µ = mean

σ = standard deviation

From the information given,

µ = 60 points

σ = 5 points

The probability of students that have scored between 60 and 65 points is expressed as

P(60 ≤ x ≤ 65)

For x = 60,

z = (60 - 60)/5 = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

For x = 65,

z = (65 - 60)/5 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

Therefore,

P(60 ≤ x ≤ 65) = 0.84 - 0.5 = 0.34

Therefore, the percent of students that have scored between 60 and 65 points is

0.34 × 100 = 34%

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step-by-step explanation:

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.