The PEFR of a group of 11 year old girls follow a normal distrubution with mean 300 1/min and standard detion 20 limin –
## **Core Concept**
The question pertains to the understanding of a normal distribution, specifically in the context of Peak Expiratory Flow Rate (PEFR) values in a group of 11-year-old girls. The normal distribution, also known as the Gaussian distribution, is characterized by its mean (μ) and standard deviation (σ). Here, the mean PEFR is given as 300 liters per minute (l/min), and the standard deviation is 20 l/min.
## **Why the Correct Answer is Right**
In a normal distribution, about 68% of the values lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% lie within three standard deviations. The correct answer likely corresponds to a specific percentage of the distribution that matches one of these rules. For instance, the range within two standard deviations of the mean (mean ± 2*standard deviation) covers approximately 95% of the values. This range would be 300 ± 2*20, which equals 300 ± 40, or 260 to 340 l/min.
## **Why Each Wrong Option is Incorrect**
- **Option A:** Without specific details on what this option states, we can't directly refute it, but any option that doesn't align with the known properties of a normal distribution (e.g., percentages of data points within certain standard deviations) would be incorrect.
- **Option B:** Similarly, lacking specifics, but if it suggests a range or percentage not consistent with standard deviation rules (e.g., more than 100% of data points within a certain range), it would be wrong.
- **Option D:** This option would be incorrect if it proposes a scenario that violates the principles of normal distribution, such as suggesting that a certain range encompasses an implausible percentage of the data given the mean and standard deviation.
## **Clinical Pearl / High-Yield Fact**
A key point to remember is that in a normal distribution, about 95% of the values lie within two standard deviations of the mean. This fact can be crucial in clinical settings for understanding the range of normal values for various physiological parameters, including PEFR. For example, knowing that a PEFR of 260-340 l/min encompasses 95% of the expected values for 11-year-old girls can help in assessing respiratory health.
## **Correct Answer:** C.