There is a population of 20000 people with mean hemoglobin being 13.5 gm% having a normal distribution. What proportion of population constitutes proportion more than 13.5 gm%?
**Core Concept**
The normal distribution of hemoglobin levels in the population is a classic example of a bell-shaped curve, where the majority of values cluster around the mean. In this case, the mean hemoglobin level is 13.5 gm%, and we want to find the proportion of the population with hemoglobin levels above this mean.
**Why the Correct Answer is Right**
To solve this problem, we need to understand that in a normal distribution, the mean, median, and mode are all equal. Since the mean is 13.5 gm%, we can use the 68-95-99.7 rule (also known as the empirical rule), which states that about 68% of the data falls within 1 standard deviation of the mean, about 95% falls within 2 standard deviations, and about 99.7% falls within 3 standard deviations. However, we are interested in the proportion above the mean, which is not directly given by this rule.
To find the proportion above the mean, we need to calculate the z-score for a hemoglobin level of 13.5 gm%. The z-score is calculated as (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. However, the standard deviation is not given in the question. Assuming a normal distribution, we can use the fact that the standard deviation is equal to the interquartile range (IQR) divided by 1.349 for a normal distribution. However, without the IQR, we can't calculate the standard deviation.
Fortunately, the question asks for the proportion above the mean, which is equivalent to 50% of the distribution above the mean, assuming a normal distribution. This is because the normal distribution is symmetric, and the mean is the point of symmetry.
**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not provided.
* **Option B:** This option is not provided.
* **Option C:** This option is not provided.
* **Option D:** This option is not provided.
**Clinical Pearl / High-Yield Fact**
In a normal distribution, the mean, median, and mode are all equal. This symmetry is a key characteristic of the normal distribution, and it's essential to remember that the normal distribution is symmetric around the mean.
**Correct Answer: . 50%**