Answer:
(a) Yes, because the probabilities add up to 1.
(b) The probability that <em>X</em> < 40 is 0.80.
Step-by-step explanation:
The probability distribution of the random variable <em>X</em> is:
<em> x</em>: 15 | 22 | 34 | 40
f (x): 0.14 | 0.40 | 0.26 | 0.20
(a)
The properties of a probability distribution are:
- 0 ≤ f (x) ≤ 1
- ∑ f (x) = 1
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.
Compute the probability of <em>X</em> < 30 as follows:
P (X < 40) = P (X = 15) + P (X = 22) + P (X = 34)
Thus, the probability that <em>X</em> < 40 is 0.80.