An art history professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 63% C: Scores below the top 37% and above the bottom 16% D: Scores below the top 84% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 77.4 and a standard deviation of 9.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

The minimum score required for an A grade is 92.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the minimum score required for an A grade.

Top 6%, so at least the 100-6 = 94th percentile, which is the value of X when Z has a pvalue of 0.94. So X when Z = 1.555. So

The minimum score required for an A grade is 92.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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i got 10.28 but that rounds up to 10.3