The probability of recall in an experiment is modeled by $P ( a \leq x \leq b ) = \int _ { a } ^ { b } \frac { 75 } { 14 } \left( \frac { x } { \sqrt { 4 + 5 x } } \right) d x , 0 \leq x \leq 1$ where x is the percent of recall. What is the probability of recalling between 50% and 70%? Round your answer to three decimal places.
A)0.243
B)0.206
C)0.650
D)0.163
E)0.832

Question

Quizplus · Accepted Answer

To find the probability of recalling between 50% and 70%, we need to evaluate the integral from $a = 0.5$ to $b = 0.7$. The integral given is $\int _ { 0.5 } ^ { 0.7 } \frac { 75 } { 14 } \left( \frac { x } { \sqrt { 4 + 5 x } } \right) d x$. Solving this integral and rounding to three decimal places gives the probability, which matches choice A, 0.243.

The Probability of Recall in an Experiment Is Modeled By P