Descriptive 5tatistics Comparing the relative sizes of data values based on their z-scores Cheyenne The local aquarium houses sharks of various species. At the aquarium, Tito is an adult male shark that is 3.1 meters long, and Lydia is an adult female shark that is 4.1 meters long. The distribution of the lengths of the adult female sharks in the aquarium is clearly skewed (not approximately symmetric). The same is true for the distribution of the lengths of the adult male sharks in the aquarium. The aquarium's adult female shark population has a mean length of 3.53 meters and a standard deviation of 0.51 meters. The aquarium's adult male shark population has a mean length of 2.67 meters and a standard deviation of 0.29 meters. (a) Find the $z$-scores of Tito's length as an adult male shark at the aquarium and Lydia's length as an adult female shark at the aquarium. Round your answers to two decimal places. z-score of Tito's length: [] $z$-score of Lydia's length: $\square$ (b) Relative to its population, which is larger? Choose the best answer based on the $z$-scores of the two lengths. Tito Lydia It is unclear which shark is larger relative to its population

Step 1 ：Given the lengths of Tito and Lydia, the mean lengths and the standard deviations of their respective populations, we need to calculate the z-scores for Tito and Lydia.

Step 2 ：The z-score is a measure of how many standard deviations an element is from the mean. To find the z-score, we subtract the mean from the element and then divide by the standard deviation.

Step 3 ：First, calculate the z-score for Tito. Subtract the mean length of the male shark population from Tito's length, then divide by the standard deviation of the male shark population. This gives a z-score of approximately 1.48.

Step 4 ：Next, calculate the z-score for Lydia. Subtract the mean length of the female shark population from Lydia's length, then divide by the standard deviation of the female shark population. This gives a z-score of approximately 1.12.

Step 5 ：Finally, compare the z-scores of Tito and Lydia. The shark with the higher z-score is larger relative to its population. In this case, Tito has a higher z-score, so Tito is larger relative to its population.

Step 6 ：Final Answer: The z-score of Tito's length is approximately \( \boxed{1.48} \) and the z-score of Lydia's length is approximately \( \boxed{1.12} \). Therefore, relative to its population, \( \boxed{\text{Tito}} \) is larger.