Government regulations dictate that for any production process involving a certain toxic chemical, the water in the output of the process must not exceed 7820 parts per million (ppm) of the chemical. For a particular process of concern, the water sample was collected by a manufacturer 25 times randomly and the sample average x was 7856 ppm. It is known from historical data that the standard deviation is 60 ppm. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) What the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem. The probability is (Round to four decimal places as needed.) (b) is an observed x = 7856 in this experiment firm evidence that the population mean for the process exceeds the government limit? Answer your question by computing P(X≥ 7856 | μ=7820). Assume that the distribution of the concentration is normal. Since P(X≥ 7856 | μ = 7820) = evidence that the population mean for the process exceeds the government limit. (Round to four decimal places as needed.) negligible, the observed x
Government regulations dictate that for any production process involving a certain toxic chemical, the water in the output of the process must not exceed 7820 parts per million (ppm) of the chemical. For a particular process of concern, the water sample was collected by a manufacturer 25 times randomly and the sample average x was 7856 ppm. It is known from historical data that the standard deviation is 60 ppm. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) What the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem. The probability is (Round to four decimal places as needed.) (b) is an observed x = 7856 in this experiment firm evidence that the population mean for the process exceeds the government limit? Answer your question by computing P(X≥ 7856 | μ=7820). Assume that the distribution of the concentration is normal. Since P(X≥ 7856 | μ = 7820) = evidence that the population mean for the process exceeds the government limit. (Round to four decimal places as needed.) negligible, the observed x
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![**Government Regulations and Toxic Chemical Levels: An Educational Overview**
Government regulations dictate that for any production process involving a certain toxic chemical, the water in the output of the process must not exceed 7820 parts per million (ppm) of the chemical. For a particular process of concern, the water sample was collected by a manufacturer 25 times randomly and the sample average x̄ was 7856 ppm. It is known from historical data that the standard deviation σ is 60 ppm. Complete parts (a) and (b) below.
**(a) What is the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem.**
The probability is [Text Field].
(Round to four decimal places as needed.)
**(b) Is an observed x̄ = 7856 in this experiment firm evidence that the population mean for the process exceeds the government limit? Answer your question by computing P(X̄ ≥ 7856 | μ = 7820). Assume that the distribution of the concentration is normal.**
Since P(X̄ ≥ 7856 | μ = 7820) = [Text Field] [Drop-down Menu] negligible, the observed x̄ [Drop-down Menu] evidence that the population mean for the process exceeds the government limit.
(Round to four decimal places as needed.)
**Notes on Graphs and Diagrams:**
- Two links are provided to access the standard normal distribution table:
- [Click here to view page 1 of the standard normal distribution table.](#)
- [Click here to view page 2 of the standard normal distribution table.](#)
- There are no direct graphs or diagrams displayed in the given text, but reference is made to statistical tables which are integral in solving the problem.
**Educational Context:**
This exercise provides a practical application of the Central Limit Theorem in environmental statistics. By understanding the probability of exceeding regulatory limits based on sample data, students can better appreciate the role of statistics in environmental compliance and public health.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b4ff4f7-2c8f-41ef-8afc-ff3d6486dbd5%2F9dec5cf4-d1d7-4cc5-af30-79dbe391cde9%2Femeohyk_processed.png&w=3840&q=75)
Transcribed Image Text:**Government Regulations and Toxic Chemical Levels: An Educational Overview**
Government regulations dictate that for any production process involving a certain toxic chemical, the water in the output of the process must not exceed 7820 parts per million (ppm) of the chemical. For a particular process of concern, the water sample was collected by a manufacturer 25 times randomly and the sample average x̄ was 7856 ppm. It is known from historical data that the standard deviation σ is 60 ppm. Complete parts (a) and (b) below.
**(a) What is the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem.**
The probability is [Text Field].
(Round to four decimal places as needed.)
**(b) Is an observed x̄ = 7856 in this experiment firm evidence that the population mean for the process exceeds the government limit? Answer your question by computing P(X̄ ≥ 7856 | μ = 7820). Assume that the distribution of the concentration is normal.**
Since P(X̄ ≥ 7856 | μ = 7820) = [Text Field] [Drop-down Menu] negligible, the observed x̄ [Drop-down Menu] evidence that the population mean for the process exceeds the government limit.
(Round to four decimal places as needed.)
**Notes on Graphs and Diagrams:**
- Two links are provided to access the standard normal distribution table:
- [Click here to view page 1 of the standard normal distribution table.](#)
- [Click here to view page 2 of the standard normal distribution table.](#)
- There are no direct graphs or diagrams displayed in the given text, but reference is made to statistical tables which are integral in solving the problem.
**Educational Context:**
This exercise provides a practical application of the Central Limit Theorem in environmental statistics. By understanding the probability of exceeding regulatory limits based on sample data, students can better appreciate the role of statistics in environmental compliance and public health.
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