A psychologist is planning a study on the effect of motivation on performance of an attention task. In this task, participants try to identify target letters in a stream of letters passing by at a rapid rate. The researcher knows from long experience that, under ordinary experimental conditions, the population of students who participate in this task identify a mean of 71 of the key letters, the standard deviation is 10, and that the distribution is approximately normal. The psychologist predicts that, if the participant is paid a dollar for each letter identified correctly, that the number correctly identified will increase to 74. The psychologist plans to test 20 participants under these conditions, using the .05 level.
Determine the mean associated with the critical z value on the distribution of means for the comparison distribution?