Continuous Random Variables Discrete Vs Continuous Discrete Continuous

Continuous Random Variables

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

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.

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

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)

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? ?

The heights of the female students at SLHS are normally distributed with a What is the z-score mean of 65 inches. What is the for the 63? standard deviation of this distribution if 18. 5% of the female students are shorter than 63 inches? P(X < 63) =. 185 -0. 9 63