We appreciate your visit to The owner of a sporting goods store is making a supply purchase for the coming month Based on past experience he has constructed a model. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We start with the model prediction that customers choose soccer balls $58\%$ of the time. In what follows, each week’s data and the combined totals are compared with the model using a small acceptable range (within $\pm 0.03$ of $0.58$, i.e. between $0.55$ and $0.61$) to decide whether the results are consistent with the model.
Below is the step-by-step solution:
────────────────────────────
Step 1. Analyze Week 1 Data
The numbers for Week 1 are:
- Soccer Balls: $85$
- Baseball Bats: $30$
- Tennis Rackets: $31$
1. Calculate the total number of items purchased in Week 1:
$$
\text{Total}_{1} = 85 + 30 + 31 = 146
$$
2. Determine the soccer ball ratio:
$$
\text{Soccer Ratio}_{1} = \frac{85}{146} \approx 0.5822
$$
Since $0.5822$ lies between $0.55$ and $0.61$, the Week 1 results are **Consistent with Model**.
────────────────────────────
Step 2. Analyze Week 2 Data
The numbers for Week 2 are:
- Soccer Balls: $110$
- Baseball Bats: $22$
- Tennis Rackets: $23$
1. Calculate the total number of items purchased in Week 2:
$$
\text{Total}_{2} = 110 + 22 + 23 = 155
$$
2. Determine the soccer ball ratio:
$$
\text{Soccer Ratio}_{2} = \frac{110}{155} \approx 0.7097
$$
Since $0.7097$ is noticeably higher than $0.61$, the Week 2 results are **Inconsistent with Model**.
────────────────────────────
Step 3. Analyze Week 3 Data
The numbers for Week 3 are:
- Soccer Balls: $64$
- Baseball Bats: $21$
- Tennis Rackets: $23$
1. Calculate the total number of items purchased in Week 3:
$$
\text{Total}_{3} = 64 + 21 + 23 = 108
$$
2. Determine the soccer ball ratio:
$$
\text{Soccer Ratio}_{3} = \frac{64}{108} \approx 0.5926
$$
Since $0.5926$ lies between $0.55$ and $0.61$, the Week 3 results are **Consistent with Model**.
────────────────────────────
Step 4. Analyze the Total of All Weeks
Combine the totals from each week:
1. Total soccer balls over 3 weeks:
$$
\text{Total Soccer Balls} = 85 + 110 + 64 = 259
$$
2. Total baseball bats over 3 weeks:
$$
\text{Total Bats} = 30 + 22 + 21 = 73
$$
3. Total tennis rackets over 3 weeks:
$$
\text{Total Rackets} = 31 + 23 + 23 = 77
$$
4. The overall total number of items is:
$$
\text{Combined Total} = 259 + 73 + 77 = 409
$$
5. Determine the overall soccer ball ratio:
$$
\text{Soccer Ratio}_{\text{Total}} = \frac{259}{409} \approx 0.6333
$$
Since $0.6333$ is above the acceptable range, the combined or **Total of all** results are **Inconsistent with Model**.
────────────────────────────
Step 5. Analyze the “3 Weeks' Results”
For this analysis, we average the three weekly soccer ratios:
1. The average of the three weekly ratios is computed as:
$$
\text{Average Ratio} = \frac{0.5822 + 0.7097 + 0.5926}{3} \approx 0.6282
$$
Since $0.6282$ is higher than $0.61$, the **3 weeks' results** are also **Inconsistent with Model**.
────────────────────────────
Final Classification:
• Week 1 results: **Consistent with Model**
• Week 2 results: **Inconsistent with Model**
• Week 3 results: **Consistent with Model**
• Total of all: **Inconsistent with Model**
• 3 weeks' results: **Inconsistent with Model**
────────────────────────────
Thus, after classifying each set of results, we place:
Under **Consistent with Model**:
- Week 1 results
- Week 3 results
Under **Inconsistent with Model**:
- Week 2 results
- Total of all
- 3 weeks' results
This completes the step-by-step solution.
Below is the step-by-step solution:
────────────────────────────
Step 1. Analyze Week 1 Data
The numbers for Week 1 are:
- Soccer Balls: $85$
- Baseball Bats: $30$
- Tennis Rackets: $31$
1. Calculate the total number of items purchased in Week 1:
$$
\text{Total}_{1} = 85 + 30 + 31 = 146
$$
2. Determine the soccer ball ratio:
$$
\text{Soccer Ratio}_{1} = \frac{85}{146} \approx 0.5822
$$
Since $0.5822$ lies between $0.55$ and $0.61$, the Week 1 results are **Consistent with Model**.
────────────────────────────
Step 2. Analyze Week 2 Data
The numbers for Week 2 are:
- Soccer Balls: $110$
- Baseball Bats: $22$
- Tennis Rackets: $23$
1. Calculate the total number of items purchased in Week 2:
$$
\text{Total}_{2} = 110 + 22 + 23 = 155
$$
2. Determine the soccer ball ratio:
$$
\text{Soccer Ratio}_{2} = \frac{110}{155} \approx 0.7097
$$
Since $0.7097$ is noticeably higher than $0.61$, the Week 2 results are **Inconsistent with Model**.
────────────────────────────
Step 3. Analyze Week 3 Data
The numbers for Week 3 are:
- Soccer Balls: $64$
- Baseball Bats: $21$
- Tennis Rackets: $23$
1. Calculate the total number of items purchased in Week 3:
$$
\text{Total}_{3} = 64 + 21 + 23 = 108
$$
2. Determine the soccer ball ratio:
$$
\text{Soccer Ratio}_{3} = \frac{64}{108} \approx 0.5926
$$
Since $0.5926$ lies between $0.55$ and $0.61$, the Week 3 results are **Consistent with Model**.
────────────────────────────
Step 4. Analyze the Total of All Weeks
Combine the totals from each week:
1. Total soccer balls over 3 weeks:
$$
\text{Total Soccer Balls} = 85 + 110 + 64 = 259
$$
2. Total baseball bats over 3 weeks:
$$
\text{Total Bats} = 30 + 22 + 21 = 73
$$
3. Total tennis rackets over 3 weeks:
$$
\text{Total Rackets} = 31 + 23 + 23 = 77
$$
4. The overall total number of items is:
$$
\text{Combined Total} = 259 + 73 + 77 = 409
$$
5. Determine the overall soccer ball ratio:
$$
\text{Soccer Ratio}_{\text{Total}} = \frac{259}{409} \approx 0.6333
$$
Since $0.6333$ is above the acceptable range, the combined or **Total of all** results are **Inconsistent with Model**.
────────────────────────────
Step 5. Analyze the “3 Weeks' Results”
For this analysis, we average the three weekly soccer ratios:
1. The average of the three weekly ratios is computed as:
$$
\text{Average Ratio} = \frac{0.5822 + 0.7097 + 0.5926}{3} \approx 0.6282
$$
Since $0.6282$ is higher than $0.61$, the **3 weeks' results** are also **Inconsistent with Model**.
────────────────────────────
Final Classification:
• Week 1 results: **Consistent with Model**
• Week 2 results: **Inconsistent with Model**
• Week 3 results: **Consistent with Model**
• Total of all: **Inconsistent with Model**
• 3 weeks' results: **Inconsistent with Model**
────────────────────────────
Thus, after classifying each set of results, we place:
Under **Consistent with Model**:
- Week 1 results
- Week 3 results
Under **Inconsistent with Model**:
- Week 2 results
- Total of all
- 3 weeks' results
This completes the step-by-step solution.
Thanks for taking the time to read The owner of a sporting goods store is making a supply purchase for the coming month Based on past experience he has constructed a model. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
