Question

A student graduated from a 2-year college with an outstanding loan of $6200 where the average debt of all 2-year colleges is $7275 with a standard deviation of $1200. Another student graduated from a university with an outstanding loan of $16700 where the average debt of all universities is $19794 with a standard deviation of $6800. Which student has a higher debt relative to their group? (4 points)

1. What formula will you use for this problem?

2. Please explain how you determined the correct formula?

• The mean and standard deviation was given.
• The information provided was a sample.
• We are comparing two debts and want to know which one has more variation.
• We want to know which debt was relatively higher among its group.
• The information provided was a population.

3. Which class was his relative position higher?

4. Please explain your conclusion.

Answer 1

1.

Z score

Z = (X-mean)/Std. deviation

2.

We want to know the distance of the student's mean from the average of the group in terms of std. deviation of the group. this formula is also used in normal distribution to calculate probability.

3.

For a 2-year college student:

z = (6200-7275)/1200

= -0.8958

For a university student:

z = (16700-19794)/6800

= -0.455

4.

Thus university student has higher debt relative to the group since -0.455 > -0.8958.

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