The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. if the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? give the answer that is closest to the exact number.

The lowest marks that a student can have and still be awarded a passing grade is 44.

Step-by-step explanation:

Given :

Mean,

Standard Deviation,

Calculation :

z score is given by,

----- (1)

Value of z corresponds to 5% is,

from equation (1) we get,

The lowest marks that a student can have and still be awarded a passing grade is 44.

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the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: