Which system of linear inequalities is represented by the graph?
Oyxx-2 and y = x + 1
O y x+1
O y sx-2 and y> x + 1
O y> x-2 and y < x + 1

(a) The probability distribution is valid.

(b) The probability that x = 30 is 0.30.

Step-by-step explanation:

The probability distribution of the random variable X is:

   x:  20   |  25  |  30   |   35

f (x): 0.20 | 0.15 | 0.30 | 0.35

(a)

The properties of a probability distribution are:

All the probability value are more than 0 and less than 1.

Compute the sum of all the probabilities as follows:

The sum of all probabilities is 1.

Thus, the probability distribution is valid.

(b)

Consider the probability distribution table.

The probability of X = 30 is,

P (X = 30) = 0.30.

Thus, the probability that x = 30 is 0.30.