Normal Distributions

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.

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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