A Poll Worker Analyzing The Ages Of Voters Found That Μ = 65 \mu=65 Μ = 65 And Σ = 5 \sigma=5 Σ = 5 . What Is A Possible Voter Age That Would Give Her Z X = 1.14 Z_x = 1.14 Z X = 1.14 ? Round Your Answer To The Nearest Whole Number.A. 59 B. 66 C. 71 D. 90

Mar 13, 2025 by ADMIN 261 views

A Poll Worker's Dilemma: Finding a Voter's Age Using the Z-Score Formula

Understanding the Z-Score Formula

In statistics, the z-score formula is used to calculate the number of standard deviations a value is away from the mean. The formula is given by:

z = (X - μ) / σ

where:

z is the z-score
X is the value of the element
μ is the mean of the dataset
σ is the standard deviation of the dataset

The Problem at Hand

A poll worker analyzing the ages of voters found that the mean age (μ) is 65 and the standard deviation (σ) is 5. The poll worker wants to find a possible voter age that would give her a z-score of 1.14.

Using the Z-Score Formula to Find the Voter's Age

To find the voter's age, we can rearrange the z-score formula to solve for X:

X = μ + (z * σ)

Substituting the given values, we get:

X = 65 + (1.14 * 5)

Calculating the Voter's Age

Now, let's calculate the voter's age:

X = 65 + 5.7 X = 70.7

Rounding the Answer to the Nearest Whole Number

Since the question asks for the answer to be rounded to the nearest whole number, we round 70.7 to 71.

Conclusion

Therefore, a possible voter age that would give the poll worker a z-score of 1.14 is 71.

Discussion

This problem demonstrates the use of the z-score formula in real-world scenarios. The z-score formula is a powerful tool in statistics that allows us to compare values across different datasets. In this case, the poll worker used the z-score formula to find a possible voter age that would give her a z-score of 1.14.

Answer Choices

A. 59 B. 66 C. 71 D. 90

The correct answer is C. 71.

Additional Information

The z-score formula is widely used in statistics and is an essential tool for data analysis. It is used in various fields, including finance, medicine, and social sciences. The z-score formula is also used in quality control to detect outliers and anomalies in a dataset.

Real-World Applications

The z-score formula has numerous real-world applications. For example, in finance, the z-score formula is used to calculate the probability of a company's bankruptcy. In medicine, the z-score formula is used to calculate the probability of a patient's recovery. In social sciences, the z-score formula is used to calculate the probability of a person's behavior.

Conclusion

In conclusion, the z-score formula is a powerful tool in statistics that allows us to compare values across different datasets. The poll worker used the z-score formula to find a possible voter age that would give her a z-score of 1.14. The correct answer is C. 71.

Understanding the Z-Score Formula

In statistics, the z-score formula is used to calculate the number of standard deviations a value is away from the mean. The formula is given by:

z = (X - μ) / σ

where:

z is the z-score
X is the value of the element
μ is the mean of the dataset
σ is the standard deviation of the dataset

Q&A Session

Q: What is the z-score formula used for?

A: The z-score formula is used to calculate the number of standard deviations a value is away from the mean. It is used in various fields, including finance, medicine, and social sciences.

Q: How do I calculate the z-score?

A: To calculate the z-score, you need to know the value of the element (X), the mean of the dataset (μ), and the standard deviation of the dataset (σ). You can use the formula: z = (X - μ) / σ

Q: What is the difference between the z-score and the standard deviation?

A: The z-score is a measure of how many standard deviations a value is away from the mean, while the standard deviation is a measure of the spread of the data.

Q: Can I use the z-score formula to find the mean or standard deviation?

A: No, the z-score formula is used to find the z-score, not the mean or standard deviation. To find the mean or standard deviation, you need to use other formulas.

Q: How do I use the z-score formula in real-world scenarios?

A: The z-score formula is used in various real-world scenarios, including finance, medicine, and social sciences. For example, in finance, the z-score formula is used to calculate the probability of a company's bankruptcy. In medicine, the z-score formula is used to calculate the probability of a patient's recovery.

Q: What is the significance of the z-score in statistics?

A: The z-score is a significant concept in statistics as it allows us to compare values across different datasets. It is used to detect outliers and anomalies in a dataset.

Q: Can I use the z-score formula to find the probability of an event?

A: Yes, the z-score formula can be used to find the probability of an event. By using a z-table or a calculator, you can find the probability of a value being within a certain range of the mean.

Q: What is the relationship between the z-score and the normal distribution?

A: The z-score is related to the normal distribution, as it is used to calculate the probability of a value being within a certain range of the mean. The normal distribution is a probability distribution that is symmetric about the mean.

Q: Can I use the z-score formula to find the median or mode?

A: No, the z-score formula is used to find the z-score, not the median or mode. To find the median or mode, you need to use other formulas.

Q: How do I interpret the z-score in a real-world scenario?

A: To interpret the z-score in a real-world scenario, you need to understand the context of the data and the z-score formula. For example, if the z-score is 1.14, it means that the value is 1.14 standard deviations away from the mean.

Conclusion

In conclusion, the z-score formula is a powerful tool in statistics that allows us to compare values across different datasets. The z-score formula is used in various real-world scenarios, including finance, medicine, and social sciences. By understanding the z-score formula and its significance, you can use it to make informed decisions in various fields.