Question

a. the probability of x being no more than a:
p(x ≥ a)
p(x = a)
p(x ≤ a)
p(x > a)
p(x < a)
b. the probability of x being at least a:
p(x = a)
p(x > a)
p(x ≥ a)
p(x ≤ a)
p(x < a)
c. the probability of x being at most a:
p(x ≥ a)
p(x = a)
p(x > a)
p(x ≤ a)
p(x < a)
d. the probability of x being no less than a:
p(x ≤ a)
p(x > a)
p(x = a)
p(x < a)
p(x ≥ a)
e. the probability of x being more than a:
p(x ≤ a)
p(x ≥ a)
p(x = a)
p(x > a)
p(x < a)
f. the probability of x being exactly a:
p(x ≤ a)
p(x = a)
p(x ≥ a)
p(x < a)

Explanation:

Step1: Interpret "no more than"

"No more than a" means $X$ is less than or equal to $a$, so the probability is $P(X\leq a)$.

Step2: Interpret "at least"

"At least a" means $X$ is greater than or equal to $a$, so the probability is $P(X\geq a)$.

Step3: Interpret "at most"

"At most a" means $X$ is less than or equal to $a$, so the probability is $P(X\leq a)$.

Step4: Interpret "no less than"

"No less than a" means $X$ is greater than or equal to $a$, so the probability is $P(X\geq a)$.

Step5: Interpret "more than"

"More than a" means $X$ is greater than $a$, so the probability is $P(X > a)$.

Step6: Interpret "exactly"

"Exactly a" means $X=a$, so the probability is $P(X = a)$.

Answer:

a. $P(X\leq a)$
b. $P(X\geq a)$
c. $P(X\leq a)$
d. $P(X\geq a)$
e. $P(X > a)$
f. $P(X = a)$