Answer: a. Yes.
c. 0.85
d. 0.60
e. 0.92
Step-by-step explanation:
Given discrete probability distribution :
x 15 22 34 40
P(X = x) 0.08 0.52 0.25 0.15
a. The sum of the all probabilities in an distribution is 1.
here, Total sum = P(X= 15) + P(X=22) + P(X=34) + P(X=40)
= 0.08 + 0.52+ 0.25 +0.15=1
∴ Yes , It is a valid probability distribution.
c. The probability that the random variable X is less than 39 : P(X<39)
= P(X= 15) + P(X=22) + P(X=34)
= 0.08 + 0.52+ 0.25 = 0.85
∴ The probability that the random variable X is less than 39 = 0.85
d. The probability that the random variable X is strictly between 9 and 24
:P( 9<X<24)= P(X= 15) + P(X=22)
= 0.08 + 0.52 =0.60
∴ The probability that the random variable X is strictly between 9 and 24=0.60
e. The probability that the random variable X is greater than 17 : P(X>17)
= P(X=22) + P(X=34) + P(X=40)
=0.52+ 0.25 +0.15=0.92
∴ The probability that the random variable X is greater than 17=0.92
