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.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

answer;

the correct answer

just use google you beautiful person.

have a nice day < 3