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Using z-scores
If we convert a standard score (x-value) to a
z-score, then we can use our standard
normal distribution procedures.
z
x

x    z 
Example
Men have a sitting heights that are normally
distributed with a mean of 36.0 in. and a standard
deviation of 1.4 in.
The Honda Civic has a headroom of 39 in. What is
the probability that a randomly selected man won’t
fit in the Civic?
If you want to design a car so that 97% of men can
fit it in, what should the headroom be?
Example
Replacement times for CD players are
normally distributed with a mean of 7.1
years and a standard deviation of 1.4 years.
If you want to provide a warranty so that only
2% of the CD players will be replaced
before the warranty expires, what is the
time length of the warranty?
Homework
5.3: 1, 7, 13, 17