Transcript Linear transformation rule

LINEAR TRANSFORMATION RULE
When adding a constant to a random
variable, the mean changes but not the
standard deviation.
When multiplying a constant to a random
variable, the mean and the standard
deviation changes.
An appliance repair shop charges a $30 service call
to go to a home for a repair. It also charges $25 per
hour for labor. From past history, the average length
of repairs is 1 hour 15 minutes (1.25 hours) with
standard deviation of 20 minutes (1/3 hour).
Including the charge for the service call, what is the
mean and standard deviation for the charges for
labor?
  30  25(1.25)  $61.25
1
  25   $8.33
3
RULES FOR COMBINING TWO
VARIABLES
To find the mean for the sum (or difference), add (or
subtract) the two means
To find the standard deviation of the sum (or
differences), ALWAYS add the variances, then take
the square root.
Formulas:
 a  b   a  b
a b  a  b
2
a
 a b    
2
b
If variables are independent
Bicycles arrive at a bike shop in boxes. Before they can be
sold, they must be unpacked, assembled, and tuned
(lubricated, adjusted, etc.). Based on past experience, the
times for each setup phase are independent with the
following means & standard deviations (in minutes). What
are the mean and standard deviation for the total bicycle
setup times?
Phase
Mean
SD
Unpacking
Assembly
Tuning
3.5
21.8
12.3
0.7
2.4
2.7
T  3.5  21.8  12.3  37.6 minutes
T  0.7 2  2.42  2.7 2  3.680 minutes