The majority of the data is normally distributed if there are enough subjects. For instance, if you collected test scores of only a few honor students, the data will most likely not be normally distributed because you would have a sample that did not represent the entire population. But the identical test scores (for honor students) collected from all schools in a state will result in a normal distribution.
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.
I don't understand it that is why I am asking for help. I do not expect you to do it for me but maybe show an example?
Example of a population that is expected to be normally distributed:
Let's consider the heights of adult males in a particular country as an example of a population that would be normally distributed. We expect this distribution to be normal because height is influenced by a combination of various genetic and environmental factors that are likely to act independently and additively. With a large enough sample size, the heights of a population would follow a bell-shaped curve.
Subset of the population that would not be normally distributed:
Now, let's consider a subset of the identified population, specifically professional basketball players from that country. The distribution of heights within this subset would not be normally distributed due to a specific selection bias. Professional basketball players tend to be taller than the average population, as height is an advantageous attribute for the sport. This subset would have a right-skewed distribution, meaning that there would be a greater concentration of individuals towards the taller end of the height spectrum.
The distribution of heights among professional basketball players would not be a normal distribution for two reasons:
1. Selection bias: Professional basketball players are selected based on their height, which inherently skews the distribution. Those below a certain height threshold are less likely to be included, leading to a right-skewed distribution.
2. Extreme outlier effect: While the majority of individuals in the subset will still fall within a typical range (albeit skewed towards taller heights), there will also be a small number of extreme outliers who are exceptionally tall, further extending the distribution towards the right.
Therefore, in this subset, the distribution of heights among professional basketball players would be right-skewed and deviate from the normal distribution observed in the overall population.