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


Burger King Dinner Service Times Use the frequency distribution from Exercise 18 in Section 2-1 to construct a histogram. 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. Step 1: Understand the problem. A histogram is a graphical representation of data using bars of different heights. To construct the histogram, we need the frequency distribution from Exercise 18 in Section 2-1. Ensure you have the class intervals (bins) and their corresponding frequencies ready.
2. Step 2: Label the axes of the histogram. The x-axis will represent the class intervals (e.g., ranges of dinner service times), and the y-axis will represent the frequencies (e.g., the number of occurrences in each interval).
3. Step 3: Draw the bars for the histogram. For each class interval, draw a bar whose height corresponds to the frequency of that interval. Ensure the bars are adjacent to each other with no gaps, as histograms represent continuous data.
4. Step 4: Analyze the shape of the histogram. To determine if the data follows a normal distribution, check if the histogram has a bell-shaped curve. A normal distribution typically has a single peak in the center, symmetry about the center, and tails that taper off on both sides.
5. Step 5: Apply a strict interpretation of normality. Evaluate whether the histogram meets the criteria for a normal distribution. If the histogram deviates significantly from the bell-shaped curve (e.g., it is skewed, has multiple peaks, or lacks symmetry), then the data may not come from a population with 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, spread, and central tendency 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. Key properties include the mean, median, and mode being equal, and about 68% of the data falling within one standard deviation of the mean.

Criteria for Normality

The criteria for determining if a dataset follows a normal distribution include visual assessments (like histograms), statistical tests (such as the Shapiro-Wilk test), and checking for symmetry and the absence of skewness. A strict interpretation requires that the data closely aligns with the properties of a normal distribution, which can be evaluated through these methods.