Question

GRE score and undergraduate GPA (1: ≥ 3.5 and 2: < 3.5)

a) High GRE score, high GPA
b) High GRE score, low GPA
c) Low GRE score, high GPA
d) Low GRE score, low GPA

Answer 1

The x value corresponding to z = -2.25 for a population with mean (μ) = 65 and standard deviation (σ) = 4 is x = 55. The x value is calculated using the formula x = μ + (z × σ), where μ represents the mean, z denotes the z-score, and σ is the standard deviation.

Explanation:

In statistics, the z-score represents the number of standard deviations a particular data point is from the mean of a distribution. The formula to calculate the x value from a z-score is x = μ + (z × σ), where x is the data point, μ is the mean, z is the z-score, and σ is the standard deviation.

Given that the population has a mean (μ) of 65 and a standard deviation (σ) of 4, and the z-score (z) is -2.25, substituting these values into the formula gives x = 65 + (-2.25 × 4) = 65 - 9 = 55. This means that a data point located 2.25 standard deviations below the mean in this distribution corresponds to an x value of 55.

Therefore, an x value of 55 corresponds to a z-score of -2.25 in this population. It indicates that a data point with a value of 55 is 2.25 standard deviations below the mean of 65 in this particular distribution. This method allows for the translation between z-scores and actual data values within a normal distribution, aiding in statistical analysis and interpretation of data.

Answer 2

According to the provided equation, a student's GPA depends mostly on study time, which is given twice the importance of SAT scores or class attendance. To raise their GPA, a student should attend all classes and allocate more hours to study, as the SAT scores are already set and cannot be changed.a) High GRE score, high GPA

Step-by-step explanation:

A student's GPA (Grade Point Average) can be influenced by multiple factors. The equation provided, GPA = 0.25 x combined_SAT + 0.25 × class_attendance + 0.50 × hours_spent studying, suggests that the number of hours spent studying has the most impact on GPA, being assigned a weight of 0.50, which is double the weight of either combined SAT scores or class attendance, which are each given a weight of 0.25.

Given this model, the best way to raise one's GPA is by improving class attendance and, more importantly, increasing the amount of time allocated to studying. The combined SAT score is fixed once you are in college, as the SATs are typically taken prior to college admission. Therefore, to enhance GPA, a student should focus on the variables that can be changed: attending classes regularly and dedicating more time to study.a) High GRE score, high GPA