Transcript ch 6

Characteristics:
•Unimodal
•Roughly Symmetric
Notation: N(,)
Model(mean, standard deviation)
y
• Parameter versus Statistic
– Statistic: a value from hard-core data
– Parameter: numerically valued attribute of a
model. Not a summary of data (statistic).
Used to set the parameters for a model.
Z-Scores!
• Standardized values
• Tells how many standard deviations you
are away from the mean (positive = above
mean; negative = below mean.
• Has a mean of 0 and a standard deviation
of 1.
• Benefit: has no units. Enables you to
compare apples & oranges.

y  y
z
• Z-Score Formula
s
Decathlon
Event
Competitor
100 m Dash
Shot Put
Long Jump
A
10.1
66’
26’
B
9.9
60’
27’
C
10.3
63
27’3”
Mean
10
60’
26’
St. Dev
0.2
3’
6”
N(6.6lb.,1.3lb)
The army reports the distribution of
head circumference of male soldiers. It
is approximately normal with a mean of
22.8 inches and a standard deviation of
1.1 inches.
1) Sketch the Normal model
2) What percent of soldiers have a
head circumference of greater than
23.9 inches?
3) What percent of soldiers have head
circumference between 21.7 and
23.9 inches?
4) One day the sergeant, yelling
obtrusively, tells Bob that he has a
big head. Feeling insecure, Bob
goes and measures the
circumference of his head and finds
it to be 24.35cm. Is the sergeant
correct???
1) Sketch the Normal model
2) What percent of soldiers have a
head circumference of greater than
23.9 inches?
3) What percent of soldiers have head
circumference between 21.7 and
23.9 inches?
4) One day the sergeant, yelling
obtrusively, tells Bob that he has a
big head. Feeling insecure, Bob
goes and measures the
circumference of his head and finds
it to be 24.35cm. Is the sergeant
correct???
N(24mpg, 6mpg)
1) Sketch the normal
model.
2) What percent of
cars get less than
15 mpg?
3) What percent get
between 20-30
mpg?
4) More than 40mpg?
5) Describe the worst
20%.
6) Q3?
7) Describe the most
efficient 5%.
N(24mpg, 6mpg)
1) What percent get
under 20 mpg?
2) Environmentalists
want no more than
10% under 20mpg,
what is the needed
fuel efficiency if the
standard deviation
remains the same?
3) Auto makers feel
they can average
26mpg, what
standard deviation
will enable the
10%?