Question

Suppose the sample space for a continuous random variable is 0 to 400. If

Answer 1

Answer:

P(72 ≤ x ≤ 400) = 0.82. Correct: C.

Explanation:

Probability Distribution

In any probability distribution, the total probability of the sample space must be 1.

Since the sample space is given as a random variable x that takes values from 0 to 400, then:

P(0 ≤ x ≤ 400) = 1

For any value of x:

If the sample space is divided into two parts like:

P(0 ≤ x ≤ 72) and P(72 ≤ x ≤ 400), then the combined probability must be 1:

P(0 ≤ x ≤ 72) + P(72 ≤ x ≤ 400) = 1

Or, equivalently:

P(72 ≤ x ≤ 400) = 1 - P(0 ≤ x ≤ 72)

P(72 ≤ x ≤ 400) = 1 - 0.18

P(72 ≤ x ≤ 400) = 0.82

A. The value 0.92 is not correct since does not match with the value 0.82.

B. The value 0.18 is not correct since does not match with the value 0.82.

C. This is the correct value. Correct Choice

D. The value 0.982 is not correct since does not match with the value 0.82.