What If a set of grades on a statistics examination are approximately normally distributed with the mean of 74 and a standard deviation of 7.9? When:

Question

a. The lowest passing grade is the lowest 10% of the student are given F’s;
b. The highest B is the top 5% of the students are given A’s.
c. The lowest B if the top 10% of the students are given A’s and the next 25% of the students are
given B’s.

Madeline Alexander · Accepted Answer

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Hailey Anderson · Answer

undefined If a set of grades on a statistics examination is approximately normally distributed with a mean of 74 and a standard deviation of 7.9, you can use the properties of the normal distribution to answer various questions about the grades.

For example, you can find the probability that a randomly selected student scored below a certain grade, between two grades, or above a certain grade by converting the raw scores to z-scores using the formula:

$$ z = \frac{x - \mu}{\sigma} $$

Where:
- $ x $ is the raw score,
- $ \mu $ is the mean of the distribution,
- $ \sigma $ is the standard deviation of the distribution,
- $ z $ is the z-score.

Once you have the z-score, you can look up the corresponding probabilities from the standard normal distribution table or use statistical software to find the probabilities directly.

You can also calculate percentiles for specific grades, indicating the percentage of students who scored below a given grade.

Additionally, you can use the normal distribution to identify outliers or extreme scores by determining how many standard deviations away from the mean a particular score falls.

Overall, knowing the mean and standard deviation of a normally distributed set of grades allows you to analyze the distribution of scores and make various statistical inferences about the performance of students on the examination.

What If a set of grades on a statistics examination are approximately normally distributed with the mean of 74 and a standard deviation of 7.9? When:

a. The lowest passing grade is the lowest 10% of the student are given F’s; b. The highest B is the top 5% of the students are given A’s. c. The lowest B if the top 10% of the students are given A’s and the next 25% of the students are given B’s.

a. The lowest passing grade is the lowest 10% of the student are given F’s;
b. The highest B is the top 5% of the students are given A’s.
c. The lowest B if the top 10% of the students are given A’s and the next 25% of the students are
given B’s.