Question

Choose the options from the drop- downs that is true of normally distributed data.

Answer 1

I don’t see the drop‑down options — please paste them and I’ll pick which are true. Meanwhile, here are the common true properties of a normally distributed (Gaussian) variable you can use to match options:

True properties of a normal distribution
- It is continuous and defined for all real numbers (support = (−∞, ∞)).
- The PDF is bell‑shaped and symmetric about the mean.
- Mean = median = mode (center of symmetry).
- It is unimodal (one peak).
- Skewness = 0.
- Kurtosis = 3 (excess kurtosis = 0).
- Empirical rule: about 68% of values lie within ±1σ, 95% within ±2σ, and 99.7% within ±3σ of the mean.
- Characterized completely by two parameters: mean µ and variance σ².
- Linear combinations of independent normal variables are normal; sample means from a normal population are normal.
- Tails approach the horizontal axis asymptotically (never actually reach zero).

Common false statements to watch for
- “Data are bounded” — false.
- “Discrete or only integer values” — false.
- “Skewed” — false (normal is symmetric).
- “All datasets are exactly normal” — false; many real datasets are only approximately normal.

If you paste the exact drop‑down choices I’ll mark which are true.