Which statement is TRUE about Standard normal distribution curve :
The question is asking which statement is true, but the options aren't provided. However, common true statements about the standard normal distribution include that it's symmetric around the mean, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three. Also, the total area under the curve is 1, and it's unimodal.
The correct answer would likely be one of these points. For example, if an option states that the mean is 0 and standard deviation is 1, that's correct. If an option says it's symmetric, that's also correct. If someone says 95% of data is within two standard deviations, that's accurate.
Now, the incorrect options might include things like the mean being 1, or the curve being skewed, or percentages outside the empirical rule. For each of these, I need to explain why they're wrong. For example, a mean of 1 would be incorrect because the standard normal distribution specifically has a mean of 0. A skewed distribution is wrong because the normal distribution is symmetric.
The clinical pearl here is to remember the 68-95-99.7 rule for quick reference in exams. Also, noting that the standard normal distribution is used in Z-scores to compare data points from different normal distributions.
Putting it all together, the correct answer is probably an option that correctly states one of these key points. Since the user didn't provide the options, I'll have to structure the explanation around common correct and incorrect statements.
**Core Concept**
The standard normal distribution is a symmetric, bell-shaped probability distribution with a mean (μ) of 0 and standard deviation (σ) of 1. It is central to statistical inference, enabling Z-score calculations to standardize data for hypothesis testing and confidence intervals.
**Why the Correct Answer is Right**
The standard normal curve is symmetric around its mean (0), with 68.27% of data within ±1σ, 95.45% within ±2σ, and 99.73% within ±3σ. This empirical rule (68-95-99.7) is critical for interpreting probabilities and variability in normally distributed data. The curve’s total area equals 1 (100% probability), and it is unimodal with tails approaching but never touching the x-axis.
**Why Each Wrong Option is Incorrect**
**Option A:** If it states the curve is skewed left/right, it is incorrect—normality implies symmetry.
**Option B:** If it claims the mean is non-zero (e.g., μ=1), it is wrong—the standard normal distribution defines μ=0.
**Option C:** If it suggests the curve has two modes, it is false—the normal distribution is strictly unimodal.
**Clinical Pearl / High-Yield Fact**
Remember the **68-95-99.7 rule** for quick reference: