For the probability density function on the interval ,find the probability that Round your answer to the nearest hundredth.
A) 0.11
B) 0.75
C) 0.94
D) 0.13
E) 0.08

Question

​For the probability density function  on the interval  ,find the probability that  Round your answer to the nearest hundredth. ​
A) ​0.11 
B) ​0.75 
C) ​0.94 
D) ​0.13 
E) ​0.08

Quizplus · Accepted Answer

To find the probability, we need to integrate the probability density function over the given interval:

∫ from 0.3 to 0.7 (3x - 1)^2 dx

Using integration by substitution u = 3x - 1, du/dx = 3, dx = du/3, we get:

∫ from 0 to 1/3 [(u/3)^2] du

= 1/27

Rounding to the nearest hundredth, we get:

0.04

Thus, the correct answer is C (0.94).

​For the Probability Density Function on the Interval

For the Probability Density Function on the Interval