Download Applications of Normal Distributions

Applications of Normal
Distributions
Applications of Normal Distributions
In this section we work with nonstandard normal distributions (the kind
that are found in nature).
To work with nonstandard normal distributions we simply standardize
them, and use the techniques from the previous section.
or
We use our calculators!
Applications of Normal Distributions
In this section we work with nonstandard normal distributions (the kind
that are found in nature).
To work with nonstandard normal distributions we simply standardize
them, and use the techniques from 6-2.
𝑧=
𝑥−𝜇
(𝑟𝑜𝑢𝑛𝑑 𝑧 𝑠𝑐𝑜𝑟𝑒𝑠 𝑡𝑜 2 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑝𝑙𝑎𝑐𝑒𝑠)
𝜎
Applications of Normal Distributions
Converting from a nonstandard to a standard normal distribution.
1.
Sketch a normal curve, label the mean and the specific x values, then
shade the region representing the desired probability.
2.
For each relevant value x that is a boundary for the shaded region , find
the equivalent z-score.
3.
Use a calculator (normcdf(lower, upper)) or table to find the area in
the shaded region.
Applications of Normal Distributions
The typical home doorway has a height of 6 ft 8 in. or
80 in. Given that heights of men are normally
distributed with a mean of 69.0 in. And a standard
deviation of 2.8. Find the percentage of men who can
fit through a standard doorway without having to duck.
Applications of Normal Distributions
Birth weights in the U.S. are normally distributed with a
mean of 3420 g and a standard deviation of 495 g. A
hospital requires a special treatment for babies that are
less than 2450 g or more than 4390 g. What is the
percentage of babies who do not require special
treatment. Do many babies require special treatment.
Applications of Normal Distributions
Finding Values from Known Areas
1.
2.
3.
4.
Sketch a normal distribution curve, enter the given probability or
percentage in the appropriate region of the graph, and identify the x
value(s)
Use table or calculator invNorm(area to left, mean, stdev) to find the
corresponding z-score.
Convert z-score to x-value 𝑥 = 𝜇 + 𝜎𝑧.
Refer to you sketch of the normal curve to verify that the solution
makes sense in the context of the graph and in the context of the
problem
Applications of Normal Distributions
How high should doorways be if 95% of men will
fit through without bending or bumping their
head? Heights of men are normally distributed
with a mean of 69.0 in. and a standard deviation
of 2.8 in.
Applications of Normal Distributions
After considering relevant factors, a committee
recommends special treatment for birth weights
in the lowest 3% and the highest 1%. Find the
birth weights that separate the lowest 3% and
the highest 1%. Recall birth weights in the U.S.
are normally distributed with a mean of 3420 g
and a standard deviation of 495 g.
Homework!!!
• 6.2: 1- 41 eoo