A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 46 families will be between 16.3 and 17.3 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate z-value calculations to two decimal places. P(16.3
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 46 families will be between 16.3 and 17.3 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate z-value calculations to two decimal places. P(16.3
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![### Statistical Problem: Probability of Sample Mean
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 46 families will be between 16.3 and 17.3 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate z-value calculations to two decimal places.
\[ P(16.3 < \overline{X} < 17.3) = \]
### Included Interface
There is a user interface with two buttons for input:
- A text box for entering the computed probability.
- Two buttons labeled with symbols:
- \( \times \): Likely a button for performing a calculation or clearing the input.
- A circular arrow representing reset or refresh.
### Instruction
To solve the problem, you would typically use the standard normal distribution by transforming the sample mean to a z-score and then finding the probability for the given range using z-score tables or software.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2743f58a-999a-485c-8435-d316e3b49890%2F079c822e-60f9-4e68-9467-a4a1a27f7f05%2F4ahtvoj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Problem: Probability of Sample Mean
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 46 families will be between 16.3 and 17.3 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate z-value calculations to two decimal places.
\[ P(16.3 < \overline{X} < 17.3) = \]
### Included Interface
There is a user interface with two buttons for input:
- A text box for entering the computed probability.
- Two buttons labeled with symbols:
- \( \times \): Likely a button for performing a calculation or clearing the input.
- A circular arrow representing reset or refresh.
### Instruction
To solve the problem, you would typically use the standard normal distribution by transforming the sample mean to a z-score and then finding the probability for the given range using z-score tables or software.
Expert Solution

Step 1
Given information-
Population mean, µ = 17.2 pounds
Population standard deviation, σ = 2.5 pounds
Sample size, n = 46
Let, X be the amount of glass garbage generated by the American family is normally distributed.
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