The probability distribution for the random variable x follows. x f(x) 20 0.20 25 0.15 30 0.30 35 0.35 (a) Is this probability distribution valid? Explain. Since f(x) 0 for all values of x and f(x) = , this a proper probability distribution. (b) What is the probability that x = 30?

(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.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

answer: h=5.6 i don't really know how to put into words, so i though i would let you do that. i hope i was able to some

step-by-step explanation:

18 = 6(h)+1/2

18 = 6h+1/2

18-1 = 6h/2

17 = 3h

17/3 = h

h = 5.6