Analyzing the Characteristics and Assumptions of a Normal Distribution for Body Temperature Evaluation

The figure to the right shows a histogram for the body temperatures​ (in °​F) of a sample of 494 adults. Is this distribution close to​ normal? For the population of all​ adults, should body temperature have a normal​ distribution? Why or why​ not?

To determine if the body temperature distribution shown in the histogram is close to normal, we need to analyze the characteristics and assumptions of a normal distribution

To determine if the body temperature distribution shown in the histogram is close to normal, we need to analyze the characteristics and assumptions of a normal distribution.

A normal distribution, also known as a Gaussian distribution or bell-shaped curve, has several characteristics:
1. It is symmetric, meaning the left and right halves of the distribution are mirror images.
2. It is unimodal, meaning it has only one peak.
3. It follows a specific mathematical formula, known as the normal distribution function.
4. It is defined by two parameters: the mean (µ) and the standard deviation (σ).
5. The majority of data falls within ±1, ±2, and ±3 standard deviations from the mean, representing about 68%, 95%, and 99.7% of the data, respectively.
6. The frequency distribution of the data follows a specific shape, with frequencies gradually decreasing as you move away from the mean.

Looking at the given histogram, we can observe some characteristics. The distribution seems to be approximately symmetric, with a single peak. However, the distribution does not appear to follow the classic bell-shaped curve. Instead, it shows a frequency distribution where the frequencies decrease more quickly in the tails compared to a normal distribution.

In terms of the assumptions for body temperature, the normal distribution may not be entirely appropriate for the population of all adults. Body temperature can be influenced by various factors such as age, health conditions, and activity level, which may cause the distribution to deviate from a perfect normal distribution. Additionally, certain times of the day or external factors (e.g., illnesses, stress) can affect body temperature, leading to potentially skewed or non-normal distributions.

Furthermore, it is worth noting that the choice of measurement units (°Fahrenheit in this case) itself does not necessarily favor a normal distribution. Choosing a different unit of measurement, such as Celsius or Kelvin, would not fundamentally change the distribution shape.

In conclusion, while the histogram appears to have some characteristics resembling a normal distribution, it is not a perfect fit. Additionally, due to various influencing factors and potential non-normality of body temperature, the assumption that body temperature has a normal distribution for the population of all adults may not hold.

More Answers: