Answer :
Final answer:
The admissions officer will need to know the mean and standard deviation of the ACT scores, as well as the desired z-score corresponding to a mean ACT score of 19.6. Additionally, knowledge of the sample size is required.
Explanation:
To find the percentage of samples of 50 students with a mean ACT score less than 19.6, the admissions officer needs the following information:
1. Mean (μ) and Standard Deviation (σ) of ACT Scores: These parameters describe the population of ACT scores. The mean represents the average ACT score, and the standard deviation measures the spread or variability of scores.
2. Z-Score: The admissions officer needs to calculate the z-score corresponding to a mean ACT score of 19.6. The z-score indicates how many standard deviations the sample mean is from the population mean.
3. Sample Size (n): The size of each sample being taken, which is 50 students in this case.
With these details, the admissions officer can use the z-score and the standard normal distribution to determine the percentage of samples with a mean ACT score less than 19.6. The z-score helps in finding the probability associated with this mean score. The officer can then use statistical tables or calculators to obtain the desired percentage.
In conclusion, the mean, standard deviation, z-score, and sample size are crucial for calculating the percentage of samples with a mean ACT score less than 19.6, which helps in assessing the likelihood of students' performance in the admissions process.
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