The marketing team at an internet music site wants a better understanding of who their customers are. They send out a survey to 25 customers (and use an incentive of $50 worth of downloads to guarantee 20 33 34 28 30 0 a high response rate) asking for demographic information. One of the variables is the customer's age. For the 25 customers, the ages are shown to the right. Complete parts a) through c). 31 31 13 28 11 37 23 44 48 26 25 23 32 36 32 35 43 44 44 48 a) Standardize the minimum and maximum ages using a mean of 31.96 and a standard deviation of 9.897. The z-score for the minimum age is and the z-score for the maximum age is (Round to three decimal places as needed.) b) Which has the more extreme z-score, the min or the max? The min z-score is more extreme. c) How old would someone with a z-score of 3 be? Someone with a z-score of 3 would be years old. (Round to three decimal places as needed.)
The marketing team at an internet music site wants a better understanding of who their customers are. They send out a survey to 25 customers (and use an incentive of $50 worth of downloads to guarantee 20 33 34 28 30 0 a high response rate) asking for demographic information. One of the variables is the customer's age. For the 25 customers, the ages are shown to the right. Complete parts a) through c). 31 31 13 28 11 37 23 44 48 26 25 23 32 36 32 35 43 44 44 48 a) Standardize the minimum and maximum ages using a mean of 31.96 and a standard deviation of 9.897. The z-score for the minimum age is and the z-score for the maximum age is (Round to three decimal places as needed.) b) Which has the more extreme z-score, the min or the max? The min z-score is more extreme. c) How old would someone with a z-score of 3 be? Someone with a z-score of 3 would be years old. (Round to three decimal places as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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![### Understanding Customer Demographics: Age Analysis
The marketing team at an internet music site aims to gain a better understanding of their customer base. To achieve this, they send out a survey to 25 customers, offering an incentive of $50 worth of downloads to ensure a high response rate. One of the variables analyzed is the customer's age. Below are the collected ages from 25 customers:
```
20, 33, 34, 28, 30,
31, 31, 13, 28, 11,
37, 23, 44, 48, 26,
25, 23, 32, 36, 32,
35, 43, 44, 44, 48
```
Next, we will standardize the minimum and maximum ages using a given mean and standard deviation and perform further analysis.
#### Provided Information
- **Mean (µ)**: 31.96
- **Standard Deviation (σ)**: 9.897
### Tasks:
#### a) Standardize the Minimum and Maximum Ages
We need to calculate the z-scores (standardized scores) for the minimum and maximum ages. The z-score formula is:
\[ Z = \frac{X - \mu}{\sigma} \]
Here, \(X\) represents the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
- **Minimum Age**: \( X_{min} = 11 \)
Calculate the z-score for the minimum age:
\[ Z_{min} = \frac{11 - 31.96}{9.897} \]
- **Maximum Age**: \( X_{max} = 48 \)
Calculate the z-score for the maximum age:
\[ Z_{max} = \frac{48 - 31.96}{9.897} \]
_Round the results to three decimal places._
#### b) More Extreme Z-Score
Determine which z-score is more extreme: the minimum (min) or maximum (max). An extreme z-score is further away from zero.
#### c) Determine Age for Z-Score of 3
Calculate the age \(X\) corresponding to a given z-score of 3.
Using the z-score formula rearranged to solve for \(X\):
\[ X = Z \cdot \sigma + \mu \]
Substitute](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ee3331d-49d8-4415-9fad-b1a8b7e7e93f%2F90c86ba0-778b-4d58-aa22-8fb53c21ca66%2Fc9d1urh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Customer Demographics: Age Analysis
The marketing team at an internet music site aims to gain a better understanding of their customer base. To achieve this, they send out a survey to 25 customers, offering an incentive of $50 worth of downloads to ensure a high response rate. One of the variables analyzed is the customer's age. Below are the collected ages from 25 customers:
```
20, 33, 34, 28, 30,
31, 31, 13, 28, 11,
37, 23, 44, 48, 26,
25, 23, 32, 36, 32,
35, 43, 44, 44, 48
```
Next, we will standardize the minimum and maximum ages using a given mean and standard deviation and perform further analysis.
#### Provided Information
- **Mean (µ)**: 31.96
- **Standard Deviation (σ)**: 9.897
### Tasks:
#### a) Standardize the Minimum and Maximum Ages
We need to calculate the z-scores (standardized scores) for the minimum and maximum ages. The z-score formula is:
\[ Z = \frac{X - \mu}{\sigma} \]
Here, \(X\) represents the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
- **Minimum Age**: \( X_{min} = 11 \)
Calculate the z-score for the minimum age:
\[ Z_{min} = \frac{11 - 31.96}{9.897} \]
- **Maximum Age**: \( X_{max} = 48 \)
Calculate the z-score for the maximum age:
\[ Z_{max} = \frac{48 - 31.96}{9.897} \]
_Round the results to three decimal places._
#### b) More Extreme Z-Score
Determine which z-score is more extreme: the minimum (min) or maximum (max). An extreme z-score is further away from zero.
#### c) Determine Age for Z-Score of 3
Calculate the age \(X\) corresponding to a given z-score of 3.
Using the z-score formula rearranged to solve for \(X\):
\[ X = Z \cdot \sigma + \mu \]
Substitute
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