A psychology professor assigns letter grades on a test according to the following scheme. A: Top 6%6% of scores B: Scores below the top 6%6% and above the bottom 55U% C: Scores below the top 45E% and above the bottom 24$% D: Scores below the top 76v% and above the bottom 6%6% F: Bottom 6%6% of scores Scores on the test are normally distributed with a mean of 70.970.9 and a standard deviation of 9.89.8. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

The numerical limits for a D grade is scores between 56 and 64.

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 numerical limits for a D grade.

Below the top 76%

Scores below X when Z has a pvalue of 1-0.76 = 0.24. So scores below X when Z = -0.705.

Above the bottom 6%

Above X when Z has a pvalue of 0.06. So above X when Z = -1.555.

The numerical limits for a D grade is scores between 56 and 64.

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step-by-step explanation: