Final answer:
Rita Keane's score, being 2 standard deviations above the mean, places her at the 97.5th percentile. This position indicates that her score surpasses approximately 97.5% of the test taker scores on the standardized test.
Step-by-step explanation:
The question is asking to identify at which percentile Rita Keane's score falls on a standardized test with a mean score of 70 and a standard deviation of 10. To find the percentile, we first need to calculate Rita's z-score, which is done by subtracting the mean from Rita's score and dividing by the standard deviation:
Z = (Rita's Score - Mean) / Standard Deviation
= (90 - 70) / 10
= 20 / 10
= 2
Rita has a z-score of 2. This z-score tells us how many standard deviations Rita's score is from the mean. In a standard normal distribution, a z-score of 2 corresponds to approximately the 97.5th percentile. This means that Rita's score is higher than approximately 97.5% of the test takers.
Interpreting Percentiles
Percentile rankings are a way to compare scores to a larger population, indicating the percentage of scores that a given score betters. Given Rita's z-score, she is at the 97.5th percentile, so option (4) is correct.
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