Standard Deviation and Normal Distribution

Introduction on Normal Distribution

by Melchor Rivano

Characteristics of Normal Distribution

• ​The curve is symmetrical.

• There are same number ​of scores above and below the mean.

• ​The mean, median and mode are the same

• The spread of ​normal distribution changes depending on the standard deviation

Multiple Choice

Which of the given histograms is approximately normally distributed?

Multiple Select

Which of the following statement are true for a normal distribution?

Select all that apply.

• The spread of the normal distribution changes depending on the mean.

• The spread of the normal distribution changes depending on the standard deviation.

• A higher mean will result in a skewed curve.

• The mean , median and mode have all the same value.

Multiple Select

Which of the following statement are true for a normal distribution?

Select all that apply.

• There are same number of scores above and below the mean.

• The curve is asymmetrical.

• The curve is symmetrical

• The fewest score lie around the mean.

Fill in the Blanks

Consider the following normal distribution.

What is the mean?

Fill in the Blanks

Consider the following normal distribution.

What is the median?

Fill in the Blanks

Consider the following normal distribution.

What is the mode?

Characteristics of Normal Distribution

​The image shows the distribution of females' height in a population.

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​32% of females lie between 157 cm and 163 cm and ​______% of females lie between 163 cm and 169 cm

Characteristics of Normal Distribution

​The image shows the distribution of females' height in a population.

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​1 standard deviation = ______ cm

Multiple Choice

The image shows the distribution of fish lengths in a pond.

61% of fish lengths lie between 16 in and 24 in and ​______% of fish lengths lie between 8 in and 16 in

• 32%

• 61%

• 7%

• 16%

Multiple Choice

The image shows the distribution of fish lengths in a pond.

3 standard deviation = ______ in

• 12

• 4

• 8

• 16

Multiple Choice

The image shows the distribution of fish lengths in a pond.

2 standard deviation = ______ in

• 12

• 4

• 8

• 16

Characteristics of Normal Distribution

​The image shows the distribution of SAT scores in a population.

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​What is the value of x on the graph?

​What is the value of y on the graph?

Application Problem on Normal Distribution

​A data set has a mean of 75 and a standard deviation of 4. What score is 2 standard deviations above the mean?

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Application Problem on Normal Distribution

​A data set has a mean of 65 and a standard deviation of 5. What score is 3 standard deviations below the mean?

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Fill in the Blanks

A set of geography exam scores are normally distributed with a mean of 75 points and a standard deviation of 10 points. What score is 3 standard deviations below the mean?

Fill in the Blanks

The mean height of 15 to 18-year-old males from Chile from 2009 to 2010 was 170 cm with a standard deviation of 6.28 cm. What score is 2.5 standard deviations above the mean?