In Exercises 9–18, construct the histograms and answer the given questions.


Hershey’s Kisses Use the frequency distribution from Exercise 20 in Section 2-1 to construct a histogram. In using a strict interpretation of the criteria for being a normal distribution, does the histogram appear to depict data from a population with a normal distribution?

Verified step by step guidance

1. Obtain the frequency distribution from Exercise 20 in Section 2-1. This table should include the class intervals (or bins) and their corresponding frequencies. Ensure you have the correct data to proceed.
2. Construct the histogram by plotting the class intervals on the x-axis and the frequencies on the y-axis. Each bar's height should correspond to the frequency of the respective class interval. Use consistent bar widths and ensure there are no gaps between bars if the data is continuous.
3. Examine the shape of the histogram. A normal distribution typically has a bell-shaped curve, which is symmetric around the mean. Look for symmetry, a single peak (unimodal), and tapering tails on both sides.
4. Compare the histogram to the strict criteria for a normal distribution. These criteria include symmetry, unimodality, and the empirical rule (approximately 68% of data within 1 standard deviation, 95% within 2, and 99.7% within 3). Assess whether the histogram aligns with these characteristics.
5. Conclude whether the histogram appears to depict data from a population with a normal distribution based on your observations. If the histogram deviates significantly from the bell-shaped curve, it may not represent a normal distribution.

Key Concepts

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is divided into intervals (bins) and the frequency of data points within each interval is represented by the height of bars. It helps visualize the shape, central tendency, and variability of the data, making it easier to identify patterns such as skewness or modality.

Normal Distribution

A normal distribution is a continuous probability distribution characterized by its bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off symmetrically. It is defined by two parameters: the mean (average) and the standard deviation (spread), and is fundamental in statistics for inferential analysis.

Criteria for Normality

The criteria for normality involve assessing whether a dataset follows a normal distribution, typically through visual inspection of histograms, Q-Q plots, or statistical tests like the Shapiro-Wilk test. Key indicators include symmetry around the mean, a single peak (unimodal), and the absence of significant outliers, which help determine if the data can be treated as normally distributed for further statistical analysis.