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The Normal Curve
Topic 8: Standardized Scores and Normal Distributions
CCLS
standards
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count
or measurement variable.
 Use the mean and standard deviation of the data set to fit
it to a normal distribution and to estimate population
percentages. Recognize that there are data sets for
which such a procedure is not appropriate. Use
calculators, spreadsheets, and tables to estimate areas
under the normal curve.
Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying
statistical experiments.
 Decide whether a specified model is consistent with
results from a given data-generating process, eg, using
simulation.
Make inferences and justify conclusions from sample
surveys, experiments, and observational studies.
 Evaluate reports based on data.
Essential
How can we use technology to work with the standard
Question
normal table and curve?
Technology http://bcs.whfreeman.com/sris/#t_730892____
Appendix B: Using Excel
Appendix C: Using Fathom
CW/HW
21, 23, 25
In the 1994-1995 NBA regular season, David Robinson
averages 27.6 points per game with a standard deviation of
7.3 points, and the distribution of his PERFORMANCES
can be modeled by a Normal distribution.
a. Sketch what this distribution should look like be drawing
a Normal curve and labeling the mean, mean ±1SD, and
mean ±2SD.
b. Calculate and interpret he z-score for the game where
he scored only 11 points.
c. Without doing any additional calculations, would you
describe a PERFORMANCE of 11 points as unusually
low? Explain.
d. If he played in 81 games, in about how many games do you
The Normal Curve
think he scored between 20 and 30 points?
The Normal Curve
Name: ______________________________
Probability & Statistics
1.
Date: _____
CW/HW #33
In 2004, the distribution of runs scored for Major League Baseball
players with a minimum of 500 plate appearances had a mean of 84.5
runs, with a standard deviation of 18.6 runs.
a. Sketch what this distribution would look like if the distribution
was roughly symmetric, unimodal, and bell-shaped by drawing a bellshaped curve and labeling the mean, mean ±1SD, and mean ±2SD.
b. Based on your sketch, is it plausible that the distribution of runs
scored is unimodal and symmetric? Explain.
c. Calculate and interpret the z-score of 65.9 runs.
d. What percentage of the runs scored were at least 65.9 runs?
e. What percentage of the runs scored were at most 65.9 runs?
f. What percentage of the runs scored were between 65.9 and 121.7
The Normal Curve
runs?
2. On a 2009 PGA tour, Tiger Woods had an average driving distance of
298 yards. Assuming that the distribution of his driving distances can
be modeled by a Normal distribution with a standard deviation of 12
yards,
a. About what proportion of his drives would you expect to be less
than 270 yards?
b. About what proportion of his drives would you expect to be less
than 300 yards?
c. About what proportion of his drives would you expect to be more
than 300 yards?
d. About what percent of his drives would you expect to be between
270 and 300 yards?
e. In a particular round, Tiger plans to use his driver 14 times. About
how many of his drives do you expect will go between 270 and 300
yards?