If a one-person household spends an average of $70 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $15 and the variable is normally distributed. Round your answers to the nearest hundredth. Minimum: $ Maximum: $ Submit Question
If a one-person household spends an average of $70 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $15 and the variable is normally distributed. Round your answers to the nearest hundredth. Minimum: $ Maximum: $ Submit Question
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:**
If a one-person household spends an average of $70 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $15 and the variable is normally distributed. Round your answers to the nearest hundredth.
**Inputs:**
- Minimum: $ [Input box]
- Maximum: $ [Input box]
**Submit Question Button:**
- [Submit Question]
**Explanation:**
To find the maximum and minimum amounts spent for the middle 50% (also known as the interquartile range) in a normal distribution:
1. **Identify the mean ($\mu$)**: Given as $70.
2. **Identify the standard deviation ($\sigma$)**: Given as $15.
3. **Determine the z-scores for the middle 50%**:
- The middle 50% corresponds to the 25th percentile (Q1) and the 75th percentile (Q3).
4. **Use the standard normal distribution table**:
- Q1 approximately corresponds to a z-score of -0.675.
- Q3 approximately corresponds to a z-score of 0.675.
5. **Calculate the actual values**:
- Minimum (Q1): $\mu + (z \times \sigma) = 70 + (-0.675 \times 15)$
- Maximum (Q3): $\mu + (z \times \sigma) = 70 + (0.675 \times 15)$
6. **Round the results to the nearest hundredth**.
Use the input boxes to submit the calculated minimum and maximum values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F782a469a-7766-49bc-9cc2-83eb7aa33c12%2F5689e4aa-2612-4e77-a9ce-8132c7254709%2Feo2r7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
If a one-person household spends an average of $70 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $15 and the variable is normally distributed. Round your answers to the nearest hundredth.
**Inputs:**
- Minimum: $ [Input box]
- Maximum: $ [Input box]
**Submit Question Button:**
- [Submit Question]
**Explanation:**
To find the maximum and minimum amounts spent for the middle 50% (also known as the interquartile range) in a normal distribution:
1. **Identify the mean ($\mu$)**: Given as $70.
2. **Identify the standard deviation ($\sigma$)**: Given as $15.
3. **Determine the z-scores for the middle 50%**:
- The middle 50% corresponds to the 25th percentile (Q1) and the 75th percentile (Q3).
4. **Use the standard normal distribution table**:
- Q1 approximately corresponds to a z-score of -0.675.
- Q3 approximately corresponds to a z-score of 0.675.
5. **Calculate the actual values**:
- Minimum (Q1): $\mu + (z \times \sigma) = 70 + (-0.675 \times 15)$
- Maximum (Q3): $\mu + (z \times \sigma) = 70 + (0.675 \times 15)$
6. **Round the results to the nearest hundredth**.
Use the input boxes to submit the calculated minimum and maximum values.
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