Continuous Random Variables

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Presentation transcript:

Continuous Random Variables

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.

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.

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)

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??

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