Topic 4

32問 • 1年前

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The _____________ or ______________ is a continuous probability distribution that describes data that clusters around a mean.

Normal Distribution, Gaussian Distribution

The normal distribution or Gaussian distribution is a _____________ probability distribution that describes data that clusters around a ______.

continuous, mean

The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve.

Normal Distribution, Gaussian Distribution

Normal Distribution / Gaussian Distribution : The graph of the associated probability density function is _____ shaped, with a peak at the ______ and is known as the __________ function or _________

bell, mean, Gaussian, bell curve

The _____________ was developed mathematically in 1733 by Abraham de Moivre (1667-1754) as an approximation to the binomial distribution.

normal curve

The normal curve was developed mathematically in ______ by __________________ (1667-1754) as an approximation to the __________ distribution.

1733, Abraham de Moivre, binomial

His paper was not discovered until 1924 by Karl Pearson (1857 – 1936). Pierre-Simon Laplace (1749 – 1827) used the normal curve in 1783 to describe the distribution of errors.

Abraham de Moivre

De Moivre's paper was ___ discovered until _____ by ____________ (1857 – 1936).

not, 1924, Karl Pearson

_________________ (1749 – 1827) used the normal curve in _____ to describe the distribution of errors.

Pierre-Simon Laplace, 1783

Subsequently, ______________ (1777-1855) used the normal curve to analyze astronomical data in ______.

Carl Friedrich Gauss, 1809

The normal curve is often called the ______________.

Gaussian Distribution

The term __________ curve is often used in every day activity.

bell-shaped

Among the many ____________ distributions used in the entire theory of Statistics, the ________________ is by far the most important.

continuous, normal distribution

Its study dates back to 18th century investigation into the nature of experimental errors.

Normal Distribution

Normal Distribution : Its study dates back to ____ century investigation into the nature of experimental ______.

18th, errors

It was observed that discrepancies among repeated measurements of the same physical quantity displayed by a certain kind of __________ distribution curve, referred to as the “_______________” and attributed to the laws of chance.

continuous, normal curve of errors

The graph of the normal distribution is a _______shaped curve that extends ___________ in _____ directions.

bell, indefinitely, both

The normal distribution has the following properties: The distribution curve is ____ shaped. The curve is ______________ about its center. The mean, median and the mode coincide at the _________ The normal distribution is _____________ The ________ of the curve is determined by the standard deviation of the distribution. The tails of the curve flatten out ______________ along the ___________ axis, always approaching the axis but _____ touching it. That is, the curve is _____________ to the base line. The area under the curve is ___. Thus, it represents the probability or proportion or the percentage associated with specific sets of measurement values.

bell, symmetrical, center, unimodal, width, indefinitely, horizontal, never, asymptotic, 1

_________________ is a normal probability distribution that has a mean =0 and a standard deviation =1.

Standard Normal Curve

Standard Normal Curve is a normal probability distribution that has a mean =___ and a standard deviation =___.

0, 1

The table of areas under the normal curve is also known as the __________.

z-table

The __________ is a measure of relative standing.

z-score

It is calculated by subtracting X from the measurement X and then dividing the result by s.

z-score

Z-score : It is calculated by ___________ X from the measurement X and then __________ the result by s

subtracting, divide

The final result, the _________ represents the distance between a given measurement X and the _____, expressed in standard deviations.

z-score, mean

_______ the z-score locates X within a sample or within a population.

either

If the 2 z-score are both positive and both negative in values, __________ the areas

subtract

If the 2 z-scores have different signs, ______ the two areas

add

If the required area is to the right of a negative z-score, the _______ 50% or 0.5

add

If the required area is to the left of a negative z-score, the _______ 50% or 0.5

subtract

If the required area is to the left of a positive z-score, the _______ 50% or 0.5

add

If the required area is to the right of a positive z-score, the _______ 50% or 0.5

subtract

Topic 1

Mikyii · 67問 · 1年前

Topic 1