Normal Distribution

Question 1

Symmetrical

Answer 1

Something where one side is a mirror image or reflection of the other.

Question 2

Asymptotic

Answer 2

A curve and a line that gets closer and closer but does not touch each other.

Question 3

Normal Distribution

Answer 3

a. A probability distribution of continuous random variable.
b. Shows graphical representations of random variables obtained through measurements.
c. Used to describe characteristics of populations and helps us visualize the inferences we make about the population.

Question 4

1733

Answer 4

Normal Distribution was first discovered by De Moivre (English Mathematician).

Question 5

1777

Answer 5

Later applied in natural and social sciences by Laplace (French Mathematician).

Question 6

Other Terms for Normal Distribution

Answer 6

Also known as Gaussian distribution in honor of Karl Friedrich Gauss (1809).

Question 7

Properties of Normal Distribution (5)

Answer 7

a. The normal curve is bell-shaped.
b. The curve is symmetrical about the vertical line which contains the mean.
c. The mean, median, and mode are equal and coincide at the center of the distribution.
d. The width of the curve is determined by the standard deviation of the distribution.
The curve is asymptotic with respect to the horizontal axis,
e. The total area under the normal curve is 1 or 100%.

Question 8

Properties of Normal Distribution (7)

Answer 8

a. The graph is a continuous curve and has a domain -∞ < X < ∞.
b. The graph is asymptotic to the x-axis. The value of the variable gets closer and closer but will never be equal to 0.
c. The highest point on the curve occurs at x = µ (mean).
d. The curve is symmetrical about the mean.
e. The total area in the normal distribution under the curve is equal to 1.
f. In general, the graph of a normal distribution is a bell-shaped curve with two inflection points, one on the left and another on the right. Inflection points are the points that mark the change in the curve’s concavity.
g. Every normal curve corresponds to the “empirical rule” (also called the 68 - 95 - 99.7% rule).

Question 9

Empirical Rule

Answer 9

a. 68.3% falls within 1 standard deviation of the mean.
b. 95.4% falls within 2 standard deviations of the mean
c. 99.7% of the area under falls within 3 standard deviations of the mean.