The teacher of a Data Management class, in which the class average is 68% with a standard deviation of 8.5%, has offered to help up to 10% of the students after school with their projects. Using the normal distribution, how should the teacher decide who will get help? Explain.

The teacher of a Data Management class, in which the class average is 68% with a standard deviation of 8.5%, has offered to help up to 10% of the students after school with their projects. Using the normal distribution, how should the teacher decide who will get help? Explain.

The teacher of a Data Management class, in which the class average is 68% with a standard deviation of 8.5%, has offered to help up to 10% of the students after school with their projects. Using the normal distribution, how should the teacher decide who will get help? Explain

To decide which students should get help, the teacher can use the concept of standard deviations from the mean in a normal distribution.

Step 1: Calculate the Z-score for a student's grade.

The Z-score represents the number of standard deviations a student's grade is away from the mean. The formula to calculate the Z-score is:

Z = (X - μ) / σ

Where:
Z is the Z-score,
X is the student's grade,
μ is the mean (68% in this case),
σ is the standard deviation (8.5% in this case).

For example, let's say a student has a grade of 75%:

Z = (75 - 68) / 8.5

Step 2: Look up the corresponding probability in the Z-table.

The Z-table, also known as the Standard Normal Distribution Table, provides the probability of a given Z-score occurring in the standard normal distribution curve.

For example, if the Z-score is 0.88, you would find the corresponding probability of 0.8106 in the Z-table. This probability represents the area under the curve up to that Z-score.

Step 3: Determine the cutoff point for receiving help.

The teacher can determine a cutoff point for receiving help based on either a specific Z-score or a desired probability.

For example, if the teacher decides to offer help to the top 10% of students, they would find the Z-score that corresponds to a probability of 0.90 in the Z-table. This Z-score represents the cutoff point. Any student with a Z-score equal to or higher than this cutoff point would receive help.

Step 4: Identify the students eligible for help.

Finally, the teacher can compare the Z-scores of all the students' grades to the cutoff point to determine which students are eligible to receive help. Students with a Z-score greater than or equal to the cutoff point would be selected for assistance.

By using the normal distribution and Z-scores, the teacher can objectively determine which students should receive help based on their grades' performance relative to the class average.