Suppose the standard error of the estimate for predicted grade point average GPA) is 0.2 grade units. Suppose a student has a predicted GPA of 2.90. Approximately what is the probability that the student will achieve a GPA of 3.3 or higher?
A) .5 percent
B) 2.5 percent
C) 10 percent
D) cannot be computed

Question

Quizplus · Accepted Answer

The probability that the student will achieve a GPA of 3.3 or higher can be found using the Z-score formula, which is $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (3.3 GPA), $\mu$ is the mean (predicted GPA of 2.9), and $\sigma$ is the standard deviation (standard error of 0.2). Calculating the Z-score gives $Z = \frac{3.3 - 2.9}{0.2} = 2$. Looking up a Z-score of 2 in a standard normal distribution table gives an area to the left of Z of approximately 0.9772, meaning there's about a 97.72% chance of getting a GPA less than 3.3. Therefore, the probability of getting a GPA of 3.3 or higher is about 1 - 0.9772 = 0.0228 or 2.28%, which is approximately 2.5%.

Suppose the Standard Error of the Estimate for Predicted Grade