Question

the random variable x has the following discrete probability distribution.
x | 10 | 11 | 12 | 13 | 14
p(x) | 0.3 | 0.1 | 0.3 | 0.2 | 0.1
since the values that x can assume are mutually exclusive events, the event {x ≤ 12} is the union of three mutually exclusive events, {x = 10} ∪ {x = 11} ∪ {x = 12}

4

...

a. find p(x ≤ 12)
p(x ≤ 12) = 0.7

b. find p(x > 12)
p(x > 12) = \square

Explanation:

Step1: Recall Probability Rule

For a discrete random variable, the sum of all probabilities is 1, and \( P(x > 12) = 1 - P(x \leq 12) \).

Step2: Substitute Known Value

We know \( P(x \leq 12) = 0.7 \), so \( P(x > 12) = 1 - 0.7 = 0.3 \).

Answer:

\( P(x > 12) = 0.3 \)