Question

The midterm and final exam grades for a statistics course are provided in the data set below. Jaymes, a student in the class, scored 86 on both exams. Treat the given data sets as samples. Jaymes's wants to know which grade is more unusual, the midterm grade or the final exam grade. Use Use a TI-83, TI-83 Plus, or TI-84 calculator to calculate the z-scores corresponding to each grade. Round your answer to three decimal places.

Midterm 80, 78, 85, 82, 79, 79, 78, 86, 80, 84,

final 81, 88, 68, 69, 69, 81, 82, 86, 76, 71

Answer 1

For midterm data,

Sample mean = (80+78+...+84)/10 = 81.1

Sample SD = 2.961

Now, z= (x- mean)/SD

So, z for Jaymes for the midterm exam= 86-81.1/2.961= 1.655

For Final data,

Sample mean= 77.1

Sample SD= 7.490

So here, z= (86-77.1)/7.490 = 1.188

For a standard normal distribution we know, the further the z is away from 0, the more unusual it is.

So here since 1.188 is closer to 0 than 1.655, so getting a score of 86 on the midterm exam is more unusual.