1. Continuous Random Variables

2. Discrete Vs. Continuous
Values of X are countable.
Distribution is a table or histogram.
Values of X can take on ANY value within an interval.
Are usually a measurement.
Distribution is a density curve.

3. Density Curve Properties
Always on or above the x-axis
Total area underneath the curve equals 1
The normal distribution (bell-shaped curve) is an example of a density curve.

4. Write the probability statement
The lifetime of a certain battery is normally distributed with a mean of 200 hours and a standard deviation of 15 hours. What proportion of these batteries can be expected to last less than 220 hours?
Write the probability statement
Draw & shade the curve
P(X < 220) =
.9087
NORMCDF(-9999, 220, 200,15)

5. The lifetime of a certain type of battery is normally distributed with a mean of 200 hours and a standard deviation of 15 hours. What proportion of these batteries can be expected to last more than 220 hours?
P(X>220) =
.0912
NORMCDF(220,9999, 200,15)

6. NOTE In continuous distributions: P(X = some constant #) = 0 WHY??
** Because the area of a line segment is zero!
** Is this true in a discrete distribution??

7. What is the z-score for the 63?
The heights of the female students at SLHS are normally distributed with a mean of 65 inches. What is the standard deviation of this distribution if 18.5% of the female students are shorter than 63 inches?
What is the z-score for the 63?
P(X < 63) = .185
-0.9 63