y

Characteristics:

•Unimodal

•Roughly Symmetric

Notation: N(,)

Model(mean, standard deviation)

• 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.

• Z-Score Formula

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yyz

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???

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)

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%?