Download Worksheet 4

WORKSHEET #4
STA 291
Spring 2010
Properties of the Normal Distribution:
1. The normal distribution curve is bell-shaped.
2. The mean, median, and mode are equal and located at the center of the distribution.
3. The normal distribution curve is unimodal (one mode).
4. The curve is symmetrical about the mean.
5. The curve is continuous.
6. The curve never touches the x axis.
7. The total area under the curve is equal to 1.00 (or 100%).
8. The area under the normal curve that lies within 1 standard deviation is approximately 0.68 (or
68%); within 2 standard deviations, about 0.95 (or 95%); and within 3 standard deviations, about
0.997 (or 99.7%).
Examples
1. P(0 < Z < 1.8) = _______________
2. P(Z < -1.93) = _______________
3. P(-2.48 < Z < -0.83) = _______________
4. P(-1.37 < Z < 1.68) = _______________
5. P(Z < 1.99) = _______________
6. P(Z < D) = .75, D = _______________
7. P(Z > C) = .21, C = _______________
8. P(Z < L) = .38, L = _______________
Percentiles
The pth percentile of a data set is a value Xp such that p% of the data are below Xp.
X25 = Q1 = lower quartile
X50 = Q2 = median
X75 = Q3 = upper quartile
Data set:
13
20
13
21
16
24
17
27
Q1 = ____________
71st percentile = _______________
18
31