Solve the problem. At Loop Junior College, the mean grade point average (gpa) of the current student body is 2.76 with a standard deviation of 0.64 . Compute the gpa's of each student to two decimal places. A gpa with a z-score of 1.7 . A gpa with a z-score of -2.6 .

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UpStudy AI · Accepted Answer

To find the GPA corresponding to a given z-score, you can use the formula:

$$
X = \mu + (z \cdot \sigma)
$$

where:
- $$X$$ is the value (GPA in this case),
- $$\mu$$ is the mean,
- $$z$$ is the z-score,
- $$\sigma$$ is the standard deviation.

Given:
- Mean ($$\mu$$) = 2.76
- Standard deviation ($$\sigma$$) = 0.64

### For a z-score of 1.7:

$$
X = 2.76 + (1.7 \cdot 0.64)
$$

Calculating the product:

$$
1.7 \cdot 0.64 = 1.088
$$

Now, add this to the mean:

$$
X = 2.76 + 1.088 = 3.848
$$

Rounding to two decimal places:

$$
X \approx 3.85
$$

### For a z-score of -2.6:

$$
X = 2.76 + (-2.6 \cdot 0.64)
$$

Calculating the product:

$$
-2.6 \cdot 0.64 = -1.664
$$

Now, add this to the mean:

$$
X = 2.76 - 1.664 = 1.096
$$

Rounding to two decimal places:

$$
X \approx 1.10
$$

### Summary of Results:
- GPA for z-score of 1.7: **3.85**
- GPA for z-score of -2.6: **1.10**
GPA for z-score of 1.7: 3.85 GPA for z-score of -2.6: 1.10

Solve the problem. At Loop Junior College, the mean grade point average (gpa) of the current student body is 2.76 with a standard deviation of 0.64 . Compute the gpa's of each student to two decimal places. A gpa with a z-score of 1.7 . A gpa with a z-score of -2.6 .

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