Question

the accompanying data and frequency distribution are 45 commute times to work in minutes for workers of age 16 or older in chicago. use the data and frequency distribution to construct a histogram. does it appear to be the graph of data from a population with a normal distribution? click the icon to view the commute times data and frequency distribution. the histogram so the distribution of the data is the histogram to be the graph of data from a population

Explanation:

To determine if the commute time data has a normal distribution, we analyze the histogram's shape:

Key Characteristics of a Normal Distribution:

A normal (Gaussian) distribution is symmetric (mirror - image on either side of the center), has a single peak (unimodal), and follows a bell - shaped curve (most data near the mean, tapering off evenly on both sides).

Analyzing the Histogram (General Approach, Given the Context of Commute Times):

1. Symmetry Check: For commute times, a normal - like histogram should have roughly equal frequencies on either side of the central (most frequent) commute time.
2. Peak Check: There should be one clear peak (unimodal), not multiple peaks (bimodal) or a flat distribution.

Typical Outcome for Commute Time Data (and the Implied Answer):

In practice, commute time data often has a right - skew (longer tails on the “longer commute” side, as some people have very long commutes). However, if we assume the histogram (from the problem’s context) shows a bell - shaped, symmetric, unimodal pattern, we conclude:

A normal distribution’s histogram is symmetric, unimodal, and bell - shaped. If the commute time histogram matches this (e.g., frequencies increase to a central peak then decrease symmetrically), it appears normal.

Answer:

The histogram \(\boldsymbol{\text{does (or does not, depending on the actual histogram; if following typical normal - like analysis for such problems, assume it can appear normal)}}\) appear to be the graph of data from a population with a normal distribution.

(Note: Since the actual histogram’s visual details are partially obscured, the answer depends on the histogram’s shape. For a standard “does it appear normal?” question with commute times, if the histogram is symmetric and unimodal, the answer is “Yes”; if skewed or multimodal, “No”. If we follow the problem’s intent to apply normal distribution visualization rules, the key is checking symmetry and unimodality.)