Ch. 3 - Probability

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 3 - Probability

Problem 3.3.22d

Chapter 3, Problem 3.3.22d

22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the
probability of each event. (Adapted from Ipsos)
d. Randomly selecting a British adult who feels that the move has had a fairly positive or very positive impact on Great Britain

Verified step by step guidance

Step 1: Identify the total number of respondents from the survey, which is given as 1115 British adults.

Step 2: Locate the number of respondents who feel the move has had a 'fairly positive' impact (178) and a 'very positive' impact (134) from the Pareto chart.

Step 3: Add the number of respondents for 'fairly positive' and 'very positive' impacts to find the total number of respondents who feel positively about the move. This is calculated as 178 + 134.

Step 4: Divide the total number of respondents who feel positively (from Step 3) by the total number of respondents (1115) to calculate the probability of randomly selecting a British adult who feels the move has had a fairly positive or very positive impact.

Step 5: Express the probability as a fraction, decimal, or percentage, depending on the context or requirement of the problem.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the proportion of respondents who feel a certain way about Brexit's impact, relative to the total number of surveyed individuals. For example, if 134 out of 1115 respondents feel that the impact was 'very positive,' the probability of randomly selecting someone with that opinion can be calculated as 134/1115.

Pareto Chart

A Pareto chart is a type of bar graph that represents the frequency of different categories in descending order. It is used to highlight the most significant factors in a dataset. In this case, the chart displays the responses of British adults regarding the impact of Brexit, allowing for a quick visual assessment of which opinions are most prevalent, such as 'very negative' and 'fairly negative' being the highest.

Categorical Data

Categorical data refers to data that can be divided into distinct categories, which can be nominal or ordinal. In this survey, responses about Brexit's impact are categorical, as they represent different opinions (e.g., 'very negative,' 'fairly positive'). Understanding categorical data is essential for analyzing survey results, as it informs how to interpret and visualize the data effectively.

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(Adapted from YouGov)

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Textbook Question

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c. The parent did not have major mental health issues or is a mother.

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