We have sent out everyone in a large introductory course to check whether people use seat belts. Each student has been told to look at 100 cars and count the number of people wearing seat belts. The number found by any given student is considered that student’s score. The mean score for the class is 44, with a standard deviation of 7.
(a) Diagram this distribution, assuming that the counts are normally distributed.
(b) A student who has done very little work all year has reported finding 62 seat belt users out of 100. Do we have reason to suspect that the student just made up a number rather than actually counting?