Darrin is a good piano player. when he is alone, his arousal is low and he often gets distracted and makes mistakes. when he is in a recital with strangers, he sometimes gets too nervous and aroused and also makes mistakes. his best performances are typically at home when family and friends are nearby, and his arousal level is moderate. the variations in darrin's performance can be best explained by the:

Yerkes-dodson law      

Explanation:

Yerkes-Dodson law: It was discovered by the renowned psychologists John Dillingham Dodson and Robert Yerkes in 1908.

This law illustrates that there is an association or relation between arousal and performance. The performance of a person decreases when the arousal becomes excessive. In other words, the arousal and performance are directly proportional to each other, so the increase in arousal to an optimal level can increase the performance but if the arousal goes beyond the optimal level then it decreases the performance.

The variations in Darrin's performance can be best explained by the: Yerkes-Dodson law.

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."