Ch. 3 - Describing, Exploring, and Comparing Data

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 3 - Describing, Exploring, and Comparing Data

Problem 3.3.7a

Chapter 3, Problem 3.3.7a

z Scores. In Exercises 5–8, express all z scores with two decimal places.

New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes.

a. What is the difference between the commute time of 95.0 minutes and the mean commute time?

Verified step by step guidance

Step 1: Understand the problem. We are tasked with finding the difference between a specific commute time (95.0 minutes) and the mean commute time (42.6 minutes). This is a straightforward subtraction problem.

Step 2: Write the formula for the difference. The difference can be expressed as: Difference = X - μ, where X is the specific commute time (95.0 minutes) and μ is the mean commute time (42.6 minutes).

Step 3: Substitute the given values into the formula. Replace X with 95.0 and μ with 42.6 in the formula: Difference = 95.0 - 42.6.

Step 4: Perform the subtraction operation to find the difference. This will give you the numerical value of how much the specific commute time deviates from the mean commute time.

Step 5: Interpret the result. The difference represents how many minutes the specific commute time (95.0 minutes) is above the mean commute time (42.6 minutes).

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Key Concepts

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

Z-Score

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. This standardizes scores on a common scale, allowing for comparison across different datasets.

Mean

The mean, or average, is a measure of central tendency that is calculated by summing all values in a dataset and dividing by the number of values. In the context of the commute times, the mean represents the typical commute duration, providing a baseline for comparison with individual commute times.

Standard Deviation

Standard deviation is a statistic that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It is crucial for understanding how individual commute times relate to the average.

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d. Given that the weights are from Domino sugar packets selected from a much larger population, are the weights a sample or a population?

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Textbook Question

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a. Find the missing value.

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Textbook Question

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Textbook Question

z Scores. In Exercises 5–8, express all z scores with two decimal places.

New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes.

b. How many standard deviations is that [the difference found in part (a)]?

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Textbook Question

z Scores. In Exercises 5–8, express all z scores with two decimal places.

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a. What is the difference between the highest diastolic blood pressure and the mean of the diastolic blood pressures for females?

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Textbook Question

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