Aim: How do we apply standard deviation to the normal distribution curve

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Aim How do we apply standard deviation to the
normal distribution curve?

• HW3 Complete Worksheet

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Do Now

• The grades in Mr. Ruizs statistics class are as
  follows

• What are the mean (to the nearest hundred), the
  median, and the mode for these scores?
• Without doing further calculations, can you tell
  if these scores are normally distributed?
  Explain.
• Find the variance and standard deviation to the
  nearest hundredth.

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What is a frequency polygon?

• Frequency Polygon a line graph, determined by
  connecting the midpoints of the upper edges of
  all the bars

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From the do now
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What does standard deviation really mean on the
curve?

• We start at the mean (the center of the curve)
  and to get the next intervals we count one
  standard deviation up and down and continue
  on(dont go past 3 standard deviations)

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How do we fill in the curve?

• Starting at the mean, as we move up the curve we
  continue to add one standard deviation
• As we go down the curve we subtract the standard
  deviation from the mean

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For the do now

• Mean 81.8
• Standard Deviation 9.8

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What else does the curve tell us?

• Percentages ? they are set in a curve

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How do we read the curve?

• For the do now How many scores lie within one
  standard deviation of the mean?

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Example

• Matthew Lang is a professor at the University of
  Iona Medical School where he is the director of
  the sleep laboratory. The data below comes from
  the sleeping patterns of 100 random subjects over
  a twenty-four-hour period, document in his book
  Secrets of Sleep.

• Find the mean of this data, to the nearest tenth.
  
• Find the variance of this data, to the nearest
  tenth.
• Find the standard deviation of this data, to the
  nearest tenth.
• Sketch the curve showing the distribution of this
  data.
• How many scores fall within one standard
  deviation above and below the mean?
• What percentage of the scores fall within one
  standard deviation above or below the mean?
• Compare the distribution cive for this data and
  the normal distribution. Is this sampling a
  normal distribution? Why or why not?

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Summary
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Aim How do we apply standard deviation to the
normal distribution curve?

• HW3 Complete Worksheet