Question

suppose the sample space for a continuous random variable is 0 to 50. if the area under the density curve for the variable from 0 to 38 is 0.76, what is the area under the density curve from 38 to 50?

choice

a. 0.924

b. 0.76

c. 0.34

d. 0.24

Explanation:

Step1: Recall total area property

For a continuous random variable, the total area under the density curve over the entire sample space is 1.

Step2: Calculate the desired area

Let \( A_{0 - 38} = 0.76 \) (area from 0 to 38) and \( A_{38 - 50} \) be the area from 38 to 50. We know \( A_{0 - 50}=1 \), so \( A_{38 - 50}=1 - A_{0 - 38} \). Substituting the value, we get \( 1 - 0.76 = 0.24 \).

Answer:

D. 0.24