A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effect of the drug is normally distributed, with mean µ= 38 minutes and standard deviation o= 5 minutes.

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### New Muscle Relaxant Study

A new muscle relaxant is available. Researchers from the firm developing the relaxant have conducted studies indicating that the time lapse between administration and the beginning effect of the drug is normally distributed. The distribution has a mean (µ) of 38 minutes and a standard deviation (σ) of 5 minutes.

**Study Questions:**

**(A)** The drug is administered to one randomly selected patient. What is the probability that the time it takes to take effect is 35 minutes or less?

**(B)** The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less?

**(C)** Explain the differences in the results you found.

**(D)** What types of studies and information do you think drug companies need to conduct as they develop new treatments?

### Explanation of Graphs/Diagrams:
(No specific graphs or diagrams are provided in the given text. If there were, here you would include a detailed description of any visual aids, explaining their relevance and what they depict, such as normal distribution curves or statistical result tables related to the study.) 

### Discussion:
- **Normal Distribution**: Understanding the distribution of drug efficacy times can help estimate probabilities of effectiveness under different sample conditions.
- **Statistical Analysis**: Being able to compare single patient results versus average results for a group provides insight into the consistency and reliability of the drug's performance.
- **Data Collection**: Gathering thorough information, including time to effect for various demographics and conditions, ensures a comprehensive understanding of how the drug performs across a broad patient population.

This data and these questions allow for a deep dive into biostatistics and pharmaceutical testing, critical components in the development of new medical treatments.
Transcribed Image Text:### New Muscle Relaxant Study A new muscle relaxant is available. Researchers from the firm developing the relaxant have conducted studies indicating that the time lapse between administration and the beginning effect of the drug is normally distributed. The distribution has a mean (µ) of 38 minutes and a standard deviation (σ) of 5 minutes. **Study Questions:** **(A)** The drug is administered to one randomly selected patient. What is the probability that the time it takes to take effect is 35 minutes or less? **(B)** The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? **(C)** Explain the differences in the results you found. **(D)** What types of studies and information do you think drug companies need to conduct as they develop new treatments? ### Explanation of Graphs/Diagrams: (No specific graphs or diagrams are provided in the given text. If there were, here you would include a detailed description of any visual aids, explaining their relevance and what they depict, such as normal distribution curves or statistical result tables related to the study.) ### Discussion: - **Normal Distribution**: Understanding the distribution of drug efficacy times can help estimate probabilities of effectiveness under different sample conditions. - **Statistical Analysis**: Being able to compare single patient results versus average results for a group provides insight into the consistency and reliability of the drug's performance. - **Data Collection**: Gathering thorough information, including time to effect for various demographics and conditions, ensures a comprehensive understanding of how the drug performs across a broad patient population. This data and these questions allow for a deep dive into biostatistics and pharmaceutical testing, critical components in the development of new medical treatments.
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