Let's go through the questions shown in your homework image step-by-step:

Provided Data:

The data represents the time (in minutes) that it took a random sample of students to finish an exam:

17.9  24.9  28.6  32.7  39.4  42.4  49.6  52.1
37.4  29.9  36.2  42.3  36.4  23.2  41.5  37.4
18.6  39.4  38.5  21.8  30.3  30.3  53.6  41.5
33.7  44.8  43.3  35.2  42  35.6  26  38.1
35.2  37  35.2  30.1  29.6  33  53.6  29.9

Questions:

(a) Calculate $\bar{x}$ (the mean). (b) Calculate the range. (c) Calculate $s^2$ (the sample variance). (d) Calculate $s$ (the standard deviation). (e) Calculate the z-score for a student who finished the exam in 39.4 minutes.

Let me calculate these step-by-step.Here are the results based on the provided dataHere are the results based on the provided

(a) Mean ($\bar{x}$): $35.71$ minutes (rounded to two decimal places).
(b) Range: $35.7$ minutes (difference between the highest and lowest values).
(c) Sample Variance ($s^2$): $74.95$ (rounded to two decimal places).
(d) Standard Deviation ($s$): $8.66$ minutes (rounded to two decimal places).
(e) Z-score for a student who finished the exam in 39.4 minutes: $0.43$ (rounded to two decimal places).

Would you like more details or further explanation on any part?

Here are 5 related questions you can explore:

1. How does the variance relate to the standard deviation?
2. What does the z-score indicate about the student's performance?
3. How would the mean change if the highest score were increased?
4. How can we interpret the range in the context of this data?
5. What if the sample size were larger? How would that affect the variance?

Tip: Z-scores help in comparing different data points from the same or different datasets by normalizing their values relative to the mean and standard deviation.