Question

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

the area under the density curve for the variable from 0 to 72 is 0.18, what is
the area under the density curve from 72 to 400?
A. 0.92
O B. 0.18
O C. 0.82
D. 0.982

Answer 1

Answer: .82

Step-by-step explanation:

Took the test

Answer 2

P(72 ≤ x ≤ 400) = 0.82. Correct: C.

Step-by-step 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.