Bob is a CEGEP student who got a final grade of 82. He wants to apply to the computer science program at university. The minimum requirement is to have a Zscore of 1.75 in the sample of applicants. This year, there are 100 applicants for this program with a mean final grade of 75 and a variance of 11.56. Would Bob meet the requirements?

To determine if Bob meets the requirements for the computer science program, we need to calculate Bob's Z-score based on the information provided. The formula for calculating the Z-score is:

\[
Z = \frac{X - \mu}{\sigma}
\]

Where:
- \(X\) is Bob's final grade (82),
- \(\mu\) is the mean final grade of all applicants (75),
- \(\sigma\) is the standard deviation of the applicants' final grades, which is the square root of the variance.

### Step 1: Calculate the standard deviation
We are given the variance (\(\sigma^2\)) of 11.56, so the standard deviation (\(\sigma\)) is:

\[
\sigma = \sqrt{11.56} \approx 3.4
\]

### Step 2: Calculate Bob's Z-score
Now we can calculate Bob's Z-score using the formula:

\[
Z = \frac{82 - 75}{3.4} = \frac{7}{3.4} \approx 2.06
\]

### Step 3: Compare Bob's Z-score with the requirement
The minimum Z-score required is 1.75. Since Bob's Z-score is approximately 2.06, which is greater than 1.75, he **meets the requirements** for the program.

### Conclusion:
Bob's Z-score is 2.06, so he satisfies the requirement of having a Z-score of at least 1.75 and can apply to the computer science program.

---

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How is the Z-score used in other admissions processes?
2. What does a Z-score represent in terms of distribution?
3. How could Bob improve his Z-score if needed?
4. Why is variance important in determining standard deviation?
5. What other factors, aside from grades, might influence university admission?

**Tip:** Understanding Z-scores helps you interpret where a data point stands in relation to a mean, making it useful for comparing performances across different scales.

Find out if Bob, a CEGEP student with a final grade of 82, meets the Z-score requirement of 1.75 for the computer science program at university. This guide explains how to calculate Bob's Z-score using statistical concepts such as mean, variance, and standard deviation. Suitable for Grades 11-12 students.

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