In a normal distribution, do the tails touch the horizontal axis?

In a normal distribution, do the tails touch the horizontal axis?

• A. Yes, they touch
• B. They sometimes touch
• C. No, they never touch
• D. Only at the extremes

Answer: (C)

In a normal distribution, the curve’s tails extend indefinitely and get ever closer to the horizontal axis without actually meeting it. The probability density is positive for every finite x, given by f(x) = (1/(σ√(2π))) exp(-(x-μ)^2/(2σ^2)). As x → ±∞, the density approaches zero, so it gets arbitrarily close to the axis but never reaches it at any finite point. Since the horizontal axis represents zero density, the tails do not touch it.

In a normal distribution, the curve’s tails extend indefinitely and get ever closer to the horizontal axis without actually meeting it. The probability density is positive for every finite x, given by f(x) = (1/(σ√(2π))) exp(-(x-μ)^2/(2σ^2)). As x → ±∞, the density approaches zero, so it gets arbitrarily close to the axis but never reaches it at any finite point. Since the horizontal axis represents zero density, the tails do not touch it.