Chapter 8. Continuous Probability Distributions. Probability Density Functions…. Unlike a discrete random variable which we studied in Chapter 7, a continuous random variable is one that can assume an uncountable number of values.
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Continuous Probability Distributions
The normal distribution is fully defined by two parameters:
its standard deviation andmean
The normal distribution is bell shaped and
symmetrical about the mean
Normal distributions range from minus infinity to plus infinity
1Standard Normal Distribution…
Some advice: always draw a picture!
…mean of 50 minutes and a
standard deviation of 10 minutes…
–.5 … 1
P(45 < X < 60) = P(–.5 < Z < 1) = .5328
“Just over half the time, 53% or so, a computer will have an assembly time between 45 minutes and 1 hour”
P(Z < 1.6) = .9452
P(Z > 1.6) = 1.0 – P(Z < 1.6)
= 1.0 – .9452
P(Z < 0.9)
P(Z < 1.9)
P(0.9 < Z < 1.9) = P(Z < 1.9) – P(Z < 0.9)
=.9713 – .8159
Area = .50
Area = .025
Area = .50–.025 = .4750
If you do a “reverse look-up” on Table 3 for .9750,you will get the corresponding zA = 1.96
Since P(z > 1.96) = .025, we say: z.025 = 1.96
Area under the curve value (tA) : COLUMN
Degrees of Freedom : ROW
There are different tables
for different values of A.
Make sure you start with
the correct table!!
Denominator Degrees of Freedom : ROW
Numerator Degrees of Freedom : COLUMN