🗊Презентация Introduction to normal distributions

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Introduction to normal distributions, слайд №1Introduction to normal distributions, слайд №2Introduction to normal distributions, слайд №3Introduction to normal distributions, слайд №4Introduction to normal distributions, слайд №5Introduction to normal distributions, слайд №6Introduction to normal distributions, слайд №7Introduction to normal distributions, слайд №8Introduction to normal distributions, слайд №9Introduction to normal distributions, слайд №10Introduction to normal distributions, слайд №11Introduction to normal distributions, слайд №12Introduction to normal distributions, слайд №13Introduction to normal distributions, слайд №14Introduction to normal distributions, слайд №15Introduction to normal distributions, слайд №16Introduction to normal distributions, слайд №17Introduction to normal distributions, слайд №18Introduction to normal distributions, слайд №19Introduction to normal distributions, слайд №20Introduction to normal distributions, слайд №21
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Слайд 1


Section 6-1 Introduction to Normal Distributions
Описание слайда:
Section 6-1 Introduction to Normal Distributions

Слайд 2


Section 6-1 Objectives Interpret graphs of normal probability distributions Find areas under the standard normal curve
Описание слайда:
Section 6-1 Objectives Interpret graphs of normal probability distributions Find areas under the standard normal curve

Слайд 3


Properties of Normal Distributions Normal distribution A continuous probability distribution for a random variable, x. The most important continuous probability distribution in statistics. The graph of a normal distribution is called the normal curve.
Описание слайда:
Properties of Normal Distributions Normal distribution A continuous probability distribution for a random variable, x. The most important continuous probability distribution in statistics. The graph of a normal distribution is called the normal curve.

Слайд 4


Properties of Normal Distributions The mean, median, and mode are equal. The normal curve is bell-shaped and is symmetric about the mean. The total area under the normal curve is equal to 1. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean.
Описание слайда:
Properties of Normal Distributions The mean, median, and mode are equal. The normal curve is bell-shaped and is symmetric about the mean. The total area under the normal curve is equal to 1. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean.

Слайд 5


Properties of Normal Distributions Between μ – σ and μ + σ (in the center of the curve), the graph curves downward. The graph curves upward to the left of μ – σ and to the right of μ + σ. The points at which the curve changes from curving upward to curving downward are called the inflection points.
Описание слайда:
Properties of Normal Distributions Between μ – σ and μ + σ (in the center of the curve), the graph curves downward. The graph curves upward to the left of μ – σ and to the right of μ + σ. The points at which the curve changes from curving upward to curving downward are called the inflection points.

Слайд 6


Means and Standard Deviations A normal distribution can have any mean and any positive standard deviation. The mean gives the location of the line of symmetry. The standard deviation describes the spread of the data.
Описание слайда:
Means and Standard Deviations A normal distribution can have any mean and any positive standard deviation. The mean gives the location of the line of symmetry. The standard deviation describes the spread of the data.

Слайд 7


Example: Understanding Mean and Standard Deviation Which normal curve has the greater mean?
Описание слайда:
Example: Understanding Mean and Standard Deviation Which normal curve has the greater mean?

Слайд 8


Example: Understanding Mean and Standard Deviation Which curve has the greater standard deviation?
Описание слайда:
Example: Understanding Mean and Standard Deviation Which curve has the greater standard deviation?

Слайд 9


Example: Interpreting Graphs The scaled test scores for the New York State Grade 8 Mathematics Test are normally distributed. The normal curve shown below represents this distribution. What is the mean test score? Estimate the standard deviation.
Описание слайда:
Example: Interpreting Graphs The scaled test scores for the New York State Grade 8 Mathematics Test are normally distributed. The normal curve shown below represents this distribution. What is the mean test score? Estimate the standard deviation.

Слайд 10


The Standard Normal Distribution Standard normal distribution A normal distribution with a mean of 0 and a standard deviation of 1.
Описание слайда:
The Standard Normal Distribution Standard normal distribution A normal distribution with a mean of 0 and a standard deviation of 1.

Слайд 11


The Standard Normal Distribution If each data value of a normally distributed random variable x is transformed into a z-score, the result will be the standard normal distribution.
Описание слайда:
The Standard Normal Distribution If each data value of a normally distributed random variable x is transformed into a z-score, the result will be the standard normal distribution.

Слайд 12


Properties of the Standard Normal Distribution The cumulative area is close to 0 for z-scores close to z = –3.49. The cumulative area increases as the z-scores increase.
Описание слайда:
Properties of the Standard Normal Distribution The cumulative area is close to 0 for z-scores close to z = –3.49. The cumulative area increases as the z-scores increase.

Слайд 13


Properties of the Standard Normal Distribution The cumulative area for z = 0 is 0.5000. The cumulative area is close to 1 for z-scores close to z = 3.49.
Описание слайда:
Properties of the Standard Normal Distribution The cumulative area for z = 0 is 0.5000. The cumulative area is close to 1 for z-scores close to z = 3.49.

Слайд 14


Example: Using The Standard Normal Table Find the cumulative area that corresponds to a z-score of 1.15.
Описание слайда:
Example: Using The Standard Normal Table Find the cumulative area that corresponds to a z-score of 1.15.

Слайд 15


Example: Using The Standard Normal Table Find the cumulative area that corresponds to a z-score of –0.24.
Описание слайда:
Example: Using The Standard Normal Table Find the cumulative area that corresponds to a z-score of –0.24.

Слайд 16


Finding Areas Under the Standard Normal Curve Sketch the standard normal curve and shade the appropriate area under the curve. Find the area by following the directions for each case shown. To find the area to the left of z, find the area that corresponds to z in the Standard Normal Table.
Описание слайда:
Finding Areas Under the Standard Normal Curve Sketch the standard normal curve and shade the appropriate area under the curve. Find the area by following the directions for each case shown. To find the area to the left of z, find the area that corresponds to z in the Standard Normal Table.

Слайд 17


Finding Areas Under the Standard Normal Curve To find the area to the right of z, use the Standard Normal Table to find the area that corresponds to z. Then subtract the area from 1.
Описание слайда:
Finding Areas Under the Standard Normal Curve To find the area to the right of z, use the Standard Normal Table to find the area that corresponds to z. Then subtract the area from 1.

Слайд 18


Finding Areas Under the Standard Normal Curve To find the area between two z-scores, find the area corresponding to each z-score in the Standard Normal Table. Then subtract the smaller area from the larger area.
Описание слайда:
Finding Areas Under the Standard Normal Curve To find the area between two z-scores, find the area corresponding to each z-score in the Standard Normal Table. Then subtract the smaller area from the larger area.

Слайд 19


Example: Finding Area Under the Standard Normal Curve Find the area under the standard normal curve to the left of z = –0.99.
Описание слайда:
Example: Finding Area Under the Standard Normal Curve Find the area under the standard normal curve to the left of z = –0.99.

Слайд 20


Example: Finding Area Under the Standard Normal Curve Find the area under the standard normal curve to the right of z = 1.06.
Описание слайда:
Example: Finding Area Under the Standard Normal Curve Find the area under the standard normal curve to the right of z = 1.06.

Слайд 21


Example: Finding Area Under the Standard Normal Curve Find the area under the standard normal curve between z = –1.5 and z = 1.25.
Описание слайда:
Example: Finding Area Under the Standard Normal Curve Find the area under the standard normal curve between z = –1.5 and z = 1.25.

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