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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.1.88b
Chapter 3, Problem 3.1.88b

88. Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is between \$21 and \$50.

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Step 1: Understand the box-and-whisker plot. The box-and-whisker plot visually represents the distribution of stock prices. The box spans from the first quartile (Q1) to the third quartile (Q3), and the whiskers extend to the minimum and maximum values. The median is marked within the box.
Step 2: Identify the relevant range. From the plot, the stock prices between \$21 and \(50 correspond to the first quartile (Q1 = \)21) and the third quartile (Q3 = \$50). This range includes the interquartile range (IQR), which represents the middle 50% of the data.
Step 3: Calculate the probability. Since the box-and-whisker plot divides the data into quartiles, the probability of a stock price falling within the interquartile range (between \$21 and \$50) is equal to the proportion of data within this range. This proportion is 50% because the IQR contains half of the data.
Step 4: Interpret the result. The probability of selecting a stock price between \$21 and \$50 is equivalent to the proportion of data within the interquartile range, which is 50%.
Step 5: Verify the understanding. Ensure that the interpretation aligns with the visual representation of the box-and-whisker plot, confirming that the range \$21 to \$50 corresponds to the middle 50% of the data.

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Key Concepts

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

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of a dataset that displays its minimum, first quartile, median, third quartile, and maximum. The 'box' shows the interquartile range (IQR), which contains the middle 50% of the data, while the 'whiskers' extend to the minimum and maximum values. This visualization helps in understanding the distribution and spread of the data.
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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 refers to the chance of randomly selecting a stock price that falls within a specified range, calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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Interquartile Range (IQR)

The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) in a dataset, representing the range of the middle 50% of the data. It is a key measure of statistical dispersion, indicating how spread out the values are, and is crucial for determining the probability of a stock price falling within a specific range.
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Related Practice
Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.

(Adapted from YouGov)

b. Find the probability that neither adult U.S. citizen says that Barack Obama was the best president in U.S. history."

Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

b. Find the probability that none of the six have type O+ blood."

Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

24. Knowing a Person Who Was Murdered In a sample of 11,771 children ages 2 to 17, 8% have lost a friend or relative to murder. Four children are selected at random. (Adapted from University of New Hampshire)

b. Find the probability that none of the four has lost a friend or relative to murder."

Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.

(Adapted from YouGov)

c. Find the probability that at least one of the two adult U.S. citizens says that Barack Obama was the best president in U.S. history."

Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

c. Find the probability that at least one of the two probable voters would like entertainers to address social and political issues."

Textbook Question

19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census

Bureau)

c. Randomly selecting someone who is not 60 years or over