Construction About 63% of the residents in a town are in favor of building a new high school. One hundred five residents are randomly selected. What is the probability that the sample proportion in favor of building a new school is less than 55%? Interpret your result.
Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 53m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample2h 19m
- 10. Hypothesis Testing for Two Samples3h 22m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
Problem 2.T.5
Textbook Question
"According to data from the city of Toronto, Ontario, Canada, there were nearly 112,000 parking infractions in the city for December 2020, with fines totaling over 5,500,000 Canadian dollars. The fines (in Canadian dollars) for a random sample of 105 parking infractions in Toronto, Ontario, Canada, for December 2020 are listed below. (Source: City of Toronto)


In Exercises 1–5, use technology. If possible, print your results.
Draw a histogram for the data. Does the distribution appear to be bell-shaped?"

1
Step 1: Organize the data into intervals (bins). For example, you can group the fines into intervals such as 30-50, 51-100, 101-150, and so on. This helps in creating a histogram.
Step 2: Count the frequency of fines within each interval. For instance, count how many fines fall within the range of 30-50, 51-100, etc.
Step 3: Use technology or graphing software to plot the histogram. On the x-axis, represent the intervals (bins), and on the y-axis, represent the frequency of fines within each interval.
Step 4: Analyze the shape of the histogram. Check if the distribution appears symmetric and bell-shaped, or if it is skewed to the left or right.
Step 5: Interpret the results. If the histogram is bell-shaped, it suggests that the data follows a normal distribution. If not, describe the observed pattern (e.g., skewness or uniformity).

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Histogram
A histogram is a graphical representation of the distribution of numerical data. It consists of bars that represent the frequency of data points within specified ranges, known as bins. The height of each bar indicates how many data points fall within that range, allowing for a visual assessment of the data's distribution shape, such as normal, skewed, or uniform.
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Distribution Shape
The shape of a distribution refers to the way data points are spread across different values. Common shapes include bell-shaped (normal distribution), skewed (left or right), and uniform. Understanding the distribution shape is crucial for statistical analysis, as it influences the choice of statistical tests and the interpretation of results.
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Bell-Shaped Distribution
A bell-shaped distribution, also known as a normal distribution, is characterized by its symmetric shape, where most data points cluster around a central peak and taper off equally on both sides. This shape is significant in statistics because many statistical methods assume normality, making it essential to identify whether a dataset follows this pattern for accurate analysis.
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