Transcript Normal Curves Introduction

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Statistics: Chapter 6
Z scores review, Normal Curve Introduction
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Do Now:
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Complete the Beijing Olympics worksheet given to you when
you entered class.
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This will be an extended do now and I will collect it. You may
work in table groups
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Normal Models
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Normal Models are appropriate for distributions whose
shape is uni-modal and symmetric.
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“Bell shaped curve”
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Symbols
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N(mean, standard deviation)
The normal model with mean 0 and standard deviation of 1 is
called the standard normal model (or standard normal
distribution)
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Symmetric Uni-Model Data
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So we said that symmetric, unimodal data can be
standardized into a normal model….
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So don’t claim a normal model with skewed data.
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Is anything actually ever completely normal?
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Normal Models
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The 68 – 95- 99.7 Rule (Empirical Rule)
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+ Sketch Normal Models using the 6895-99.7 Rule
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Birth weights of babies N(7.6 lb, 1.3 lb)
+ Sketch Normal Models using the 6895-99.7 Rule
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ACT Scores at a certain college, N(21.2, 4.4)
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Do Now
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Create a list in your calculator with the following numbers:
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4
3
10
12
8
9
3
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Calculating Standard Deviation on
a Calculator
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Put all your data into a list
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Under the STAT CALC menu, select 1-VAR STATS and hit
ENTER
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Specify the location of your data, created a command like 1VAR STATS L1.
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Hit ENTER again
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Normal Models
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The 68 – 95- 99.7 Rule (Empirical Rule)
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Example: This is a practice
problem in your packet***
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A forester measured 27 of the trees in a large wood that is up for
sale. He found a mean diameter of 10.4 inches and a standard
deviation of 4.7 inches. Suppose that these trees provide an
accurate description of the whole forest and the normal model
applies
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N(36, 4)
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What percent of data are between 32 and 40?
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What percent above the mean are between 36 and 40?
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What percent of data are between 28 and 44?
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What range contains 99.7% of data?
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What range contains 47.5% below the mean?
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Where would the top 16% of data be?
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What percent of data is outside 24 and 48?
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Helmet Sizes
 The
army reports that the distribution of
head circumference among male soldiers is
approximately normal with a mean of 22.8
inches and a standard deviation of 1.1
inches.
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What percent of soldiers have a head circumference greater than
23.9in?
A head circumference of 23.9 inches would be what percentile?
What percent of soldiers have a head circumference between
20.6 and 23.9inches?
What interval below the mean would contain 13.5% of soldiers?
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Driving Speed
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Suppose it takes you 20 minutes, on average, to drive to
school with a standard deviation of 2 minutes. Suppose a
normal model is appropriate for the distribution of driving
times.
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How often will you arrive at school in less than 22 minutes?
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How often will it take you more than 24 minutes?
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Do you think the distribution of your driving times is unimodal
and symmetric in general?
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What does this say about the accuracy of your predictions?
Explain.
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Practice
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Try some on your own! As always, call me over if you are
confused!
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Exit Ticket
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A company that manufactures rivets believes the shear
strength (in pounds) is modeled by N(500, 50).
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Draw and label the normal model (just sketch the curve)
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Would it be safe to use these rivets in a situation requiring a shear
strength of 750 pounds? Explain.
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About what percent of these rivets would you expect to fall below
900 pounds?
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Rivets are used in a variety of applications with varying shear
strength requirements. What is the maximum shear strength for
which you would feel comfortable approving this company rivets?
Explain your reasoning.