Final answer:
The student's question relates to the analysis of the normal distribution of heights. Using examples such as the mean height of 15-to 18-year-old Chilean males in different years, one can understand how normal distribution is described and used to estimate population characteristics, such as average height, with a certain level of confidence.
Step-by-step explanation:
The question is concerned with the normal distribution of heights among certain age groups. In statistical terms, normal distribution is a probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
For example, the mean height of 15-to 18-year-old males from Chile from 1984 to 1985 was 172.36 cm with a standard deviation of 6.34 cm, and these heights are distributed according to normal distribution, denoted by Y~ N(172.36, 6.34). Similarly, the average height from 2009 to 2010 for the same group was 170 cm with a standard deviation of 6.28 cm, denoted by X~ N(170, 6.28).
When considering how many male students to measure to estimate the mean height with a certain level of confidence, one would need to consider the standard deviation and the desired confidence interval. For instance, if you want to estimate the average height of young adult males to within 1 inch with 93 percent confidence and the standard deviation is known to be 2.5 inches, the required sample size can be determined using appropriate statistical formulas or tables.