Identify an example of a population that you would expect to be normally distributed. Explain why, according to you, it would be normally distributed. Then, describe a subset of the population you identified and explain why it would not be normally distributed and what the distribution would look like.
Try human heights and heights of a basketball team.
One example of a population that you would expect to be normally distributed is the heights of adult females. The reason for this is that height in humans is influenced by a combination of genetic and environmental factors, which can lead to a distribution that approximates a normal curve.
To determine if a population is normally distributed, you would typically collect a large sample of data and create a histogram or a density plot. The shape of the distribution can then be assessed visually, or statistically using tests such as the Anderson-Darling or Shapiro-Wilk tests.
Now, let's consider a subset of the population of adult females: professional basketball players. Despite being part of the same larger population, the heights of professional basketball players would not be normally distributed. This is because professional basketball players tend to be taller than the average population, often falling into a narrower range of high heights. This would result in a distribution that is skewed to the right, with a longer tail on the right side of the graph.
The distribution of heights among professional basketball players would likely display a positively skewed distribution, indicating that there are fewer players below the average height but a greater concentration of players at the taller heights.
To confirm this, you can collect data on the heights of professional basketball players, create a histogram or density plot, and observe the skewness of the distribution. Additionally, statistical tests for normality mentioned earlier can be employed to provide a more objective assessment of normality.