Final answer:
To calculate the minimum score required for an A grade, find the z-score corresponding to the 91st percentile of a normally distributed set of test scores with a given mean and standard deviation, and apply the score formula.
Step-by-step explanation:
The question requires determining the minimum score on a test to get an A grade when scores are normally distributed, with a top 9% cutoff. Given that the test scores have a mean of 75.8 and a standard deviation of 8.1, we need to find the z-score that corresponds to the 91st percentile (which is 100% - 9%). After obtaining the z-score, we would then use the z-score formula to solve for the raw score.
To find the z-score corresponding to the top 9% of a normal distribution, one could use a z-table or a calculator like the TI-83 or TI-84. However, it's important to note that the provided 90th percentile value of 69.4 seems incorrect based on the given mean and standard deviation. We'll use the correct process instead.
Once the z-score is identified, the formula to calculate the actual test score is: score = mean + (z-score * standard deviation). By applying this formula and rounding to the nearest whole number, we can determine the minimum score needed for an A grade.