Use the following probability distribution in order to answer the probabilities that follow. x P(X = x) 1 0.05 2 0.22 3 0.35 4 0.30 5 0.08 (a) Find P(X = 2).

P(X = 2) = 0.22.

Step-by-step explanation:

We are given with the following probability distribution below;

          X                                         P(X)

          1                                          0.05

          2                                         0.22

          3                                         0.35

          4                                         0.30

          5                                        0.08    

       Total                                       1        

As the sum of all the probabilities is equal to 1, which means that this is a valid probability distribution.

Now, from the table above P(X = 2) = 0.22.

Hence, the probability that the X is equal to 2 is 0.22 or 22%.

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: