Suppose an exam had an average (mean) score of 55% and a standard deviation of 15%.

Question

Suppose an exam had an average (mean) score of 55% and a standard deviation of 15%.

 

Table 6.3 Curving Grades

A      1.5 standard deviations above the mean or higher

B      0.5 to 1.5 standard deviations about the mean

C      within 0.5 standard deviation of the mean

D      0.5 to 1.5 standard deviations below the mean

F       1.5 standard deviation below the mean or lower

 

If the teacher curved grades using the bell curve as in Table 6.3, what score would be necessary to receive an "A"? How about a "B"? And how about a "C"?

(Fill in the blanks below and round your answers to 1 decimal place.)

We would need to get a score of at least ____% to receive an A.

We would need to get a score between ____% and ____% to receive a B.

We would need to get a score between ____% and ___% to receive a C.

Answer 1

Let's start by taking away the percentages and just calling the mean 55, with a standard deviation of 15 and a top score of 100. It's exactly the same, but in my mind it's easier to think it through that way.

 

An A is any score more than 1.5 standard deviations above the mean. Let's solve for the lowest score that can be an A with this equation, where A is the score, m is the mean and s is the standard deviation:

 

A = m + 1.5s

 

We know what m and s are, so we'll plug those in:

 

A = 55 + 1.5(15)

 

Mupltiply:

 

A = 55 + 22.5

 

Add:

 

A = 77.5

 

So any score of 77.5 or higher is an A. Seems low, that must be a hard test.

 

 

 

To find out what score would be a B, we need to solve 2 equations - one for the lowest B score, and one for the highest B score. They'll both use the same setup as the first one.

 

The equation for the highest B score is:

 

B = 55 + 1.5(15)

 

That's actually the same equation that we used for A, so we know the answer is 77.5

 

The equation for the lowest b score is:

 

b = 55 + 0.5(15)

 

I trust you to be able to work it out from there. Given these steps, can you solve C on your own?