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Applications of the Normal
Curve
I. Finding area/prob/percent
A. z = x – mu/s to determine z.
Round z to 2 dec. places. Look up
area.
1. If problem says “higher than,”
subtract area from 1.
a. ex. SAT is normally
distributed with mean of 1000 and
standard deviation of 200. Find
prob. That a student will score
higher than 1300.
i. identify values: mu = 1000, s
= 200, x = 1300
ii. Solve z = xmu/s. z = 1.50
iii. Look up area = .9332.
1.9332 = .0668
2. If prob. Says “between,” solve
z score twice.
a. ex. Find prob. That student
will score between 900 and 1200.
i. identify values: mu = 1000, s
= 200, x = 1200, 900
ii. Calculate 2 z scores: 1.00 and
0.50
iii. Look up areas and
subtract: .8413.3035=.5328
II. Finding x score given area
B. x = mu + zs
1. ex. Applicants required to
have SAT scores in 90
th
percentile
or higher to be eligible. What
minimum score must be achieved
to be eligible?
a. Identify values: mu=1000,
s=200, area = 90.
b. Look up area and solve for x.
25=0.67, x=866
3. Life span of machine is
normally distributed w/ mean of
10.2 years and s of 1.7 years.
Manufacturer willing to replace no
more than 5% of machines. Find
length of time manufacturer
should set for guarantee.
a. identify values: mu=10.2,
s=1.7, area=.05
b. Look up area and solve for
x. .05=1.645. x=7.4
i. round values to match mean
Conf. Int. for the mean
The pop. Stand. Dev. Is known
I. obtaining z score
A. (100%  conf. lvl)/2. look up z
score
II. margin of error and conf. int.
A. E = z(s/
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 Spring '08
 Gaspar,J
 Statistics

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