Final answer:
The z-score for the sample mean of the students' GRE scores is calculated to be 0 after computing the mean and standard deviation of the scores. This result is not reflected in the provided answer choices, suggesting a possible error in the question or answer options.
Step-by-step explanation:
To calculate the z-score corresponding to the sample mean of the students' GRE scores, we need to first calculate the mean (average) and standard deviation of the given scores and then use the z-score formula:
Z = (X - μ) / σ
Mean (μ) = (160+175+163+149+153)/5 = 800/5 = 160
To find the standard deviation (σ), we use the formula:
σ = √[ Σ(xi - μ)² / N ]
With N being the number of data points:
σ = √[ (160-160)² + (175-160)² + (163-160)² + (149-160)² + (153-160)² ] / 5
σ = √[ 0 + 225 + 9 + 121 + 49 ] / 5
σ = √[ 404 / 5 ]
σ = √80.8 ≈ 8.989 (rounded to three decimal places)
Finally, the z-score for the sample mean of 160 is:
Z = (160 - 160) / 8.989 = 0/8.989 = 0
Therefore, the z-score for the sample mean is 0, which is not one of the options provided (A, B, C, D), indicating there may be an error in the question or the options given.