A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.56 lb, the mean of all of the weights is x = 2.099 lb, and the standard deviation of the weights is s= 1.101 lb. a. What is the difference between the weight of 5.56 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.56 lb to a z score. d. If we consider weights that convert to z scores between 2 and 2 to be neither significantly low nor significantly high, is the weight of 5.56 lb significant? a. The difference is lb. (Type an integer or a decimal. Do not round.) b. The difference is standard deviations. (Round to two decimal places as needed.) c. The z score is z = (Round to two decimal places as needed.) d. The highest weight is
A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.56 lb, the mean of all of the weights is x = 2.099 lb, and the standard deviation of the weights is s= 1.101 lb. a. What is the difference between the weight of 5.56 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.56 lb to a z score. d. If we consider weights that convert to z scores between 2 and 2 to be neither significantly low nor significantly high, is the weight of 5.56 lb significant? a. The difference is lb. (Type an integer or a decimal. Do not round.) b. The difference is standard deviations. (Round to two decimal places as needed.) c. The z score is z = (Round to two decimal places as needed.) d. The highest weight is
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![**Analyzing a Data Set of Household Plastic Disposals**
A data set lists weights (lb) of plastic discarded by households. The highest weight recorded is 5.56 lb. The mean of all the weights is \( \bar{x} = 2.099 \, \text{lb} \) and the standard deviation of the weights is \( s = 1.101 \, \text{lb} \).
**Questions:**
**a.** What is the difference between the weight of 5.56 lb and the mean of the weights?
**b.** How many standard deviations is that [the difference found in part (a)]?
**c.** Convert the weight of 5.56 lb to a z score.
**d.** If we consider weights that convert to z scores between –2 and 2 to be neither significantly low nor significantly high, is the weight of 5.56 lb significant?
---
**Solutions:**
**a.** The difference is __________ lb.
*(Type an integer or a decimal. Do not round.)*
**b.** The difference is __________ standard deviations.
*(Round to two decimal places as needed.)*
**c.** The z score is \( z = \) __________.
*(Round to two decimal places as needed.)*
**d.** The highest weight is [ ]
*(Dropdown options for selection)*
---
**Explanation:**
To solve these questions, follow these steps:
1. **Calculate the difference between the highest weight and the mean:**
\[
\text{Difference} = 5.56 \, \text{lb} - 2.099 \, \text{lb}
\]
2. **Determine how many standard deviations this difference represents:**
\[
\text{Standard deviations} = \frac{\text{Difference}}{s}
\]
3. **Compute the z score for the weight of 5.56 lb:**
\[
z = \frac{5.56 \, \text{lb} - 2.099 \, \text{lb}}{1.101 \, \text{lb}}
\]
4. **Evaluate the significance based on the z score:**
- If the z score is between -2 and 2, the weight is not significantly different from the mean.
- Otherwise, the weight is considered significant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78a9a2c8-87fa-4dce-a05a-3dd826ae3dea%2F6e1314e3-7085-45f9-9091-c46796ef0a17%2Fbbff5v_processed.png&w=3840&q=75)
Transcribed Image Text:**Analyzing a Data Set of Household Plastic Disposals**
A data set lists weights (lb) of plastic discarded by households. The highest weight recorded is 5.56 lb. The mean of all the weights is \( \bar{x} = 2.099 \, \text{lb} \) and the standard deviation of the weights is \( s = 1.101 \, \text{lb} \).
**Questions:**
**a.** What is the difference between the weight of 5.56 lb and the mean of the weights?
**b.** How many standard deviations is that [the difference found in part (a)]?
**c.** Convert the weight of 5.56 lb to a z score.
**d.** If we consider weights that convert to z scores between –2 and 2 to be neither significantly low nor significantly high, is the weight of 5.56 lb significant?
---
**Solutions:**
**a.** The difference is __________ lb.
*(Type an integer or a decimal. Do not round.)*
**b.** The difference is __________ standard deviations.
*(Round to two decimal places as needed.)*
**c.** The z score is \( z = \) __________.
*(Round to two decimal places as needed.)*
**d.** The highest weight is [ ]
*(Dropdown options for selection)*
---
**Explanation:**
To solve these questions, follow these steps:
1. **Calculate the difference between the highest weight and the mean:**
\[
\text{Difference} = 5.56 \, \text{lb} - 2.099 \, \text{lb}
\]
2. **Determine how many standard deviations this difference represents:**
\[
\text{Standard deviations} = \frac{\text{Difference}}{s}
\]
3. **Compute the z score for the weight of 5.56 lb:**
\[
z = \frac{5.56 \, \text{lb} - 2.099 \, \text{lb}}{1.101 \, \text{lb}}
\]
4. **Evaluate the significance based on the z score:**
- If the z score is between -2 and 2, the weight is not significantly different from the mean.
- Otherwise, the weight is considered significant.
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