In each case, consider what you know about the distribution and then explain why you would expect it to be or not to be normally distributed.
a. The lifetimes of a set of batteries manufactured by a company in your town.
b. The list of guesses of the number of marbles in a large jar is filled with marbles at a neighborhood picnic.
c. The scores at an archery contest.
d. The heights of all the 1st grade students at your school
This is asking what YOU would expect, not what we would expect.
a. The lifetimes of a set of batteries manufactured by a company in your town:
In this case, we would not expect the distribution to be normally distributed. The reason is that battery lifetimes are likely to be influenced by several factors, such as the quality of the manufacturing process, variations in usage patterns, and environmental conditions. These factors can create a non-normal distribution, as batteries may fail prematurely due to certain factors or last longer than expected due to others. Therefore, the distribution of battery lifetimes is more likely to be skewed or have a different shape than the normal distribution.
To confirm this, we could collect data on battery lifetimes from the company, organize it into a dataset, and then create a histogram or a density plot to visualize the distribution. We could also calculate summary statistics like mean and standard deviation to further analyze the shape of the distribution.
b. The list of guesses of the number of marbles in a large jar at a neighborhood picnic:
In this case, we would also not expect the distribution to be normally distributed. The reason is that people's guesses are subjective and not based on any measurement or established criteria. Each person's guess is independent and can vary greatly, resulting in a wide range of possible values.
To analyze the distribution, we could collect all the guesses and create a frequency distribution or a histogram. This would help us visualize how the guesses are distributed and identify any patterns or shapes in the data. However, since the guesses are subjective, it is unlikely that the distribution will resemble a normal distribution.
c. The scores at an archery contest:
In this case, we might expect the distribution to be approximately normally distributed. Typically, in a competition like an archery contest, the scores are influenced by a combination of skill level, practice, and other factors that can affect performance. In such cases, it is common for scores to be spread out symmetrically around a central value.
To analyze the distribution, we could collect the scores from the contest participants and create a histogram or a density plot. If the shape of the distribution is roughly bell-shaped with a central peak, it suggests a normal distribution. However, it is important to note that other factors, such as variations in shooting conditions or the presence of outliers, may affect the distribution.
d. The heights of all the 1st-grade students at your school:
In this case, we might expect the distribution to be approximately normally distributed. Human heights in a population tend to follow a roughly normal distribution, with most individuals clustering around the average height and relatively few individuals at extremes (e.g., extremely short or tall heights).
To analyze the distribution, we could collect the heights of all the 1st-grade students at the school and create a histogram or a density plot. If the distribution is bell-shaped, with the majority of heights near the mean and tapering off towards the extremes, it would suggest a normal distribution. However, it is important to note that the distribution may be affected by factors such as genetic variations or other non-normal influences, leading to potential deviations from a perfectly normal distribution.