Question

1. At the end of a particular semester, Carl took four final tests. The mean and standard deviation for each test, along with Carl’s grade on each test, are listed here. Assume that the grades on each test are normally distributed.

Test	Class mean	Class SD	Carl’s grade
French	70.4	6.3	65
History	88.2	4.1	80
Psychology	83.6	3.5	91
Statistics	75.4	8.6	85

1. Compute the z score for each test. On which test did Carl do best relative to the other students taking the test? How do you know this? What was his percentile rank for his best test?

2. On which test did Carl do the worst relative to the other students taking the test? How do you know this? What was his percentile rank for his worst test?

Answer 1

Solution:-

a)

Test	Class mean	Class SD	Carl's grade	z-score
French	70.4	6.3	65
History	88.2	4.1	80
Psychology	83.6	3.5	91
Statistics	75.4	8.6	85

Carl do best relative to other students taking the test in Psychology. Carl's z-score is highest in this subject.

z = 2.1143

P(z < 2.1143) = 0.9828

P(z < 2.1143) = 98th percentile

b)

Carl do worst relative to other students taking the test in History. Carl's z-score is highest in this subject.

z = - 2.0

P(z < - 2.0) = 0.0228

P(z < - 2.0) = 2^nd percentile