section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
Assume scores are independent
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
section 7.2 notes.notebook
January 17, 2012
How to combine normal random variables:
• The same rules for means and variances apply • After finding your new mean and standard deviation continue with the z­score calculation
Tom and George are playing the club golf tournament. Their scores vary as they play the course
repeatedly. Tom's score varies according to N(110, 10) and George varies according to N(100, 8).
lower
If they play independently, what is the probability that Tom will score higher than George?
Solution:
Find the distribution of X ­ Y.
μx-y=
σ 2x - y =
Now we want to find the probability that X < Y or X - Y < 0.
P(X - Y) < 0
Since this is normally distributed, find the z-score for our desired outcome.
section 7.2 notes.notebook
January 17, 2012
Ex. Electronic Circuit
The design of an electronic circuit calls for a 100­ohm resistor and a 250­ohm
resistor connected in series so that their resistances add. The components used are not
perfectly uniform, so that the actual resistances vary independently according to the Normal distributions. The resistance of 100­ohm resistors has mean 100 ohms
and standard deviation 2.5 ohms, while that of 250­ohm resistors has mean 250 ohms and standard deviation 2.8 ohms.
a) What is the distribution of the total resistance of the two components in series?
b) What is the probability that the total resistance lies between 345 and 355 ohms?
section 7.2 notes.notebook
January 17, 2012
Attachments
Sample Data.mht