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# Compare and interpret z-scores, Probability

Colleges typically use grade point average cutoffs to decide who graduates with honors and who is accepted into certain programs (such as teacher education, for example). Suppose at a particular college, a GPA of 3.0 is the cutoff for such a decision. The students in department A have a grade point average of 3.77 with a standard deviation of 0.43 (for all course grades in classes taken in the department in a particular academic year).

The students in department B have a grade point average of 2.65 with a standard deviation of 1.16 for that same academic year. One student has taken most of his courses from department A; another student has taken most of her courses from department B. Both students have a GPA of 3.0. Compare the z-scores of the two students.
Interpret what these z-scores mean.

The amount of cola in a 12-ounce can is uniformly distributed between 11.96 ounces and 12.05 ounces.
a. What is the mean amount per can?
b. What is the standard deviation amount per can?
c. What is the probability of selecting a can of cola and finding it has less than 12 ounces?
d. What is the probability of selecting a can of cola and finding it has more than 11.98 ounces?
e. What is the probability of selecting a can of cola and finding it has more than 11.00 ounces?

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.

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