Transcript 5-1 Random Variables and Probability Distributions

6-3
Standard Units
Areas under Normal
Distributions
As long as the data follows a
normal distribution
Conversion to a z score will be a useful way to
make observations.
What is the probability that a score will fall
between a and b?
That is, what is the probability that, for a
normal distribution with μ = 10 and σ = 2 , an
x value will fall between 11 and 14?
What would YOU do???
Ideas…
Let 11 and 14 equal a and b.
Convert them to z scores.
That gives .5 and 2.00
Lets go to the chart. How would we find the area of a
z score between .5 and 2?
Draw a picture.
Generally, you take the area of the larger = the
smaller
Left of 2
Area between
Left of .5
Lets practice with the table
At a particular ski resort, the daytime
high temperature is normally
distributed during January, with a
mean of 22º F and a standard
deviation of 10º F. You are planning to
ski there this January. What is the
probability that you will encounter
highs between 29º and 40º
How does the computer do it?
Distr: 2:normalcdf(lower, upper, μ, σ)
calculates the cumulative area.
Dist: 3:invnorm(area, μ, σ) calculates the z
score for the given area (as a decimal) to
the left of z.
*What if you are using a normal curve? What
will μ and σ be??