Let's solve each part of the problem step by step.

Part (a) - Mean Quiz Score

Kirk's quiz scores are 17, 15, 15, and 18. The mean score is calculated by finding the sum of all the quiz scores and then dividing by the number of quizzes.

1. Sum of quiz scores: $17 + 15 + 15 + 18 = 65$

2. Number of quizzes: $4$

3. Mean quiz score: $\text{Mean} = \frac{\text{Sum of quiz scores}}{\text{Number of quizzes}} = \frac{65}{4} = 16.25$

So, Kirk's mean quiz score is 16.25.

Part (b) - Score Needed on the Next Quiz

Let's denote the score Kirk needs on the next quiz as $x$. We want the mean of all five quizzes to be 16.

1. Sum of the current quiz scores: $65$

2. Adding the score $x$ for the next quiz: $65 + x$

3. Mean of all five quizzes should be 16: $\frac{65 + x}{5} = 16$

4. Solve for $x$: $65 + x = 16 \times 5 = 80$ $x = 80 - 65 = 15$

So, Kirk must score 15 on the next quiz to achieve a mean quiz score of 16 points.

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Would you like further details or have any questions? Here are 5 related questions to explore:

1. What would Kirk's mean score be if he scored 20 on the next quiz?
2. If Kirk scored 10 on the next quiz, what would his new mean score be?
3. How would the mean change if one of his current quiz scores was lower?
4. What is the range of his current quiz scores?
5. What is the median of Kirk's current quiz scores?

Tip: The mean is sensitive to each data point, so even one low or high score can significantly affect it.