Question

5. Is the Normal Curve Asymptopic to the y-axis? 6. Is the Normal Curve Asymmetric ? 7. Is the Normal Curve Skewed? 8. Where are the inflection points? Yes or No Yes or No 9. What does the area under the Standard Normal Curve equal to? 10. Draw a picture to explain the empirical rule.

Answer 1

5. No

Asymptotic to the x-axis, i.e., the curve comes infinitely close to the x-axis without touching it.

6. No

Normal curve is symmetric around y axis

7. No

data are symmetric about the mean. The normal distribution has a skewness of zero.

8. Infletion points

has two inflection points (where the second derivative of f is zero and changes sign), located one standard deviation away from the mean, namely at x= u - $\sigma$ and x= u + $\sigma$

9.

Area under standard curve is unity

10.

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts:

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviations.
• 99.7% fall within three standard deviations.

The rule is also called the 68-95-99 7 Rule or the Three Sigma Rule.

% 2.35% 1506" 13.5% 34% 2.35% 13.5% ぐー0.15% 34% 68% 95% 99.7%