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Review
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.
 Represent data with plots on the real number line (dot
plots, histograms, and box plots).
 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.
Interpret linear models
 Distinguish between correlation and causation.
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.
For example, a model says a spinning coin falls heads up
with probability 0.5. Would a result of 5 tails in a row cause
you to question the model?
Make inferences and justify conclusions from sample
surveys, experiments, and observational studies.
 Evaluate reports based on data.
Review
Name: ______________________________
Probability & Statistics
1.
Date: _____
CW/HW #35
According to the Centers for Disease Control and Prevention, the
heights of three-year-old females can be modeled by a Normal
distribution with a mean of 94.5 centimeters and a standard
deviation of 4 centimeters.
a. Sketch what this distribution should look like by drawing a
Normal curve and labeling the mean, mean ±1SD, and mean
±2SD.
b. Between which two heights would you expect the middle 68% of
three-year-olds to be?
c. Is it likely that Brooke (a three-year-old) will be 82cm tall?
Explain.
d. In a school of 30 three-year-old females, about how many will be
between 86.5cm and 102.5cm tall?
e. Calculate and interpret the z-score for Macy, who was 100cm tall
at age 3.
f. Macy’s older brother, Brody, is 12 years old and 158 centimeters
tall. The mean height for 12-year-old males is 149 centimeters,
with a standard deviation of 7.9 centimeters. Who is taller,
relatively speaking, Macy or Brody?
Review
Explain:
2.
g. In a school that has 30 three-year-old females, about how many
will be between 90 and 100 centimeters tall?
In baseball, when would a strike-out be
a. a good thing?
b. a bad thing?
3.
In the 2010 Winter Olympics in Vancouver, the mean distance of ski
jumpers in the final round on the normal hill was 100.5 meters, with a
standard deviation of 3.3 meters. The distribution can be modeled by
a Normal distribution.
a. On the normal hill, the middle 95% of the jumpers flew between
what two distances?
b. Estimate the proportion of jumpers that flew over 100 meters on
the normal hill.
c. To be at the 80th percentile of distances on the normal hill,
about how far would a jumper need to fly?