A collage math professor informs her students that rather than curving final grades, she will replace each student's lowest test score with the next ot lowest test score, and then re-average the rest grades. If Leeza has test scores of 86, 92, 81, 64, and 83, by how many points does her final test average change based on the professor's policy?

Answer

To solve the problem step by step, we will follow the instructions given by the professor and calculate Leeza's final test average before and after the policy change.

### Step 1: List Leeza's test scores
Leeza's test scores are: 86, 92, 81, 64, and 83.

### Step 2: Arrange the test scores in ascending order
We need to arrange the scores from the lowest to the highest:
- 64, 81, 83, 86, 92

### Step 3: Calculate the original average
To find the original average, we sum all the test scores and divide by the number of tests.

\[ \text{Sum of scores} = 64 + 81 + 83 + 86 + 92 = 406 \]

\[ \text{Original average} = \frac{406}{5} = 81.2 \]

### Step 4: Identify the lowest and the second lowest scores
The lowest score is 64, and the second lowest score is 81.

### Step 5: Replace the lowest score with the second lowest score
According to the professor's policy, we replace the lowest score (64) with the second lowest score (81). The new set of scores becomes:
- 81, 81, 83, 86, 92

### Step 6: Calculate the new average
Now, we calculate the new average with the modified scores.

\[ \text{New Sum of scores} = 81 + 81 + 83 + 86 + 92 = 423 \]

\[ \text{New average} = \frac{423}{5} = 84.6 \]

### Step 7: Calculate the change in average
To find the change in average, we subtract the original average from the new average.

\[ \text{Change in average} = 84.6 - 81.2 = 3.4 \]

### Final Answer
The final test average changes by **3.4 points**.

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