The lengths of a professor's classes has a continuous uniform distribution between 49.29 min and 55.55 min. If one such class is randomly selected, find P54

52.6704

Step-by-step explanation:

The lengths of a professor's classes has a continuous uniform distribution between 49.29 min and 55.55 min

Let x = 49.29, y=55.55

Percentile(P) = 54/100 = 0.54

P54 = x+(y-x)p

P54 = 49.29 + (55.55-49.29)*0.54

P54 = 49.29 + 6.26*0.54

P54 = 49.29 + 3.3804

P54 = 52.6704

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: