Reviewing Normal Distributions and Z-scores
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from Math IIIREVIEWING NORMAL DISTRIBUTIONS AND
Z-SCORES
You will need:• White board &
marker• Calculator• Z-score Table• FFM Sheet
(eventually)
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The Standard Normal Distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To more easily compute the probability of a particular observation given a normally distributed variable, we can transform any normal distribution to this standard normal distribution using the following formula:
; ; When you fi nd this value for a given value, it is referred
to as the z-score. The z-score is a standard score for a data value that
indicates the number of standard deviations that the data value is away from its respective mean.
REMINDER:
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a.) What data value corresponds to a z-score of 1.5?
1.) GIVEN A NORMAL DISTRIBUTION WITH A
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b.) What data value corresponds to a z-score of ?
1.) GIVEN A NORMAL DISTRIBUTION WITH A
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Calculate the z-score for:
a.) X = 65
2.) GIVEN A NORMAL DISTRIBUTION WITH A
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Calculate the z-score for:
b.) X = 90
2.) GIVEN A NORMAL DISTRIBUTION WITH A
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Calculate the z-score for:
c.) X = 82.5
2.) GIVEN A NORMAL DISTRIBUTION WITH A
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Determine the X value which corresponds to the following z-scores:
a.) Z =
HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.
3.) GIVEN A NORMAL DISTRIBUTION WITH A
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Determine the X value which corresponds to the following z-scores:
b.) Z = 0.75
HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.
3.) GIVEN A NORMAL DISTRIBUTION WITH A
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Determine the X value which corresponds to the following z-scores:
c.) Z = 1.9
HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.
3.) GIVEN A NORMAL DISTRIBUTION WITH A
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Using the empirical rule,
a.) what percent of the data falls between and ?
b.) what x-values would correspond to (a) to contain that same percentage of data?
4.) GIVEN A NORMAL DISTRIBUTION WITH A
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Using the empirical rule,
c.) what percent of the data falls between and ?
d.) what x-values would correspond to (c) to contain that same percentage of data?
4.) GIVEN A NORMAL DISTRIBUTION WITH A
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Using the empirical rule,
e.) What percent of the data falls to the LEFT of ?
4.) GIVEN A NORMAL DISTRIBUTION WITH A
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Using the empirical rule,
f.) What percent of the data falls to the LEFT of ?
4.) GIVEN A NORMAL DISTRIBUTION WITH A
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Using the empirical rule,
g.) What percent of the data falls to the RIGHT of ?
4.) GIVEN A NORMAL DISTRIBUTION WITH A
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In a normal distribution with and ,
1.) find X if 2.) find P() = _____ 3.) P 48.2)
FFM 8/16/13:
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Section 9.2, pg. 588-590# 9.20#9.22#9.24#9.28
A.M. III HOMEWORK