The Normal Distribution: Worksheet
(Covered in class, but also read Williams, Chap. 5)
Relationships between the Sample, a Sampling Distribution and the Population
1. The normal distribution or normal curve is pictured in Williams'. Find the picture and
determine the proportions (percentages) under the curve which fall:
a. within 1 standard deviation from the mean ______________
b. within 2 standard deviations from the mean ______________
c. within 3 standard deviations from the mean ______________
Z-scores are used as an all-purpose calibration for the positions along the baseline of the
normal curve, because they can be used without any mention of the measurement being
taken for whatever variable is being described from the population. The z-score for 1
standard deviation is +1z and – 1z. Use the attached z-score table, locate the z-score for 1.0
and compare the area described in the table to your answer to 1.a. above.
What’s the difference?
Once you have mastered the z-score table, use it to find the proportion (percentage) under
the normal curve that would be determined by the center (the mean) and ±1.25 z.
_____________
How about the proportion above +2.05z? _________
How about below +2.05z? _____________
Here’s how the normal curve can be used to approximate proportions in a large population:
2. Assume the heights of women 18 to 24 are approximately normally distributed with μ=64
inches and σ=2.5 inches.
a. Draw a normal curve for this distribution, with the scale on the horizontal axes
indicating the heights at each of the major deviations.
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