Q.82 Suppose that Ricardo and Anita a... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 6: Q.82 (page 392)

Suppose that Ricardo and Anita attend different colleges. Ricardo's GPA is the same as the average GPA at his school. Anita's GPA is $0.70$ standard deviations above her school average. In complete sentences, explain why each of the following statements may be false.
a. Ricardo's actual GPA is lower than Anita's actual GPA.
b. Ricardo is not passing because his $z$ -score is zero.
c. Anita is in the $70^{th}$ percentile of students at her college.

Short Answer

Expert verified

a). Anita's average GPA, which is $0.70$ standard deviation over the average, is lower than Ricardo's average GPA, which is his college's average GPA.

b). The average GPA may be sufficient for passing. It is dependent on the passing criteria.

c). We don't know anything about the standard deviation or distribution of this GPA at Anita College in this task.

Step by step solution

Part (a) Step 1: Given Information

Ricardo's actual GPA is lower than Anita's actual GPA.

Part (a) Step 2: Explanation

Ricardo and Anita go to different universities. As a result, the average GPAs in these two universities may differ. It's possible that Anita's average GPA is lower than Ricardo's average GPA, therefore Anita's average GPA, which is $0.7$ standard deviation over the average, is lower than Ricardo's average GPA, which is his college's average GPA. As a result, one of the reasons why this statement may not be true is because of this.

Part (b) Step 1: Given Information

Ricardo is not passing because his $z$ -score is zero.

Part (b) Step 2: Explanation

Ricardo's average GPA is identical to his college GPA, his $z$ statistic is zero. However, it has no bearing on his death. This average GPA may be sufficient for passing. It is dependent on the passing criteria. As a result, it's possible that it's not true.

Part (c) Step 1: Given Information

Anita is in the $70 t h$ percentile of students at her college.

Part (c) Step 2: Explanation

We don't know anything about the standard deviation or distribution of this GPA at Anita College in this task. However, Anita's average GPA may be higher than that amount because it is higher than the average GPA in her college. One factor that may contribute to Anita's average GPA not being in the $70 t h$ percentile is that her standard deviation is too high, causing her average GPA to be higher than the $70 t h$ percentile.