Question

In: Statistics and Probability

TYPED ANSWERS ONLY Given a data set that can be graphed as a standard normal curve,...

TYPED ANSWERS ONLY

Given a data set that can be graphed as a standard normal curve, respond to the prompts below.

What defines the graph? I.e., what determines the shape of the graph and what is the relationship between these defining characteristics?
What must be done in order to transform a normal distribution of data into a standard normal distribution based on the same data?
What is the advantage of having transformed data so that it can be represented by a standard normal distribution?
We often see data points represented by either x or z. What is the relationship between them?
Why is the area under the standard normal curve above the mean always the same value?

Expert Solution

Answer :-

1) Graph :-

=> The standard Normal Curves of normal distribution is symmetrical and bell-shaped in which the mean, median and mode are equal. It is a central components of inferential statics.

• The shape of the graphic is determined by the data points, if the mean, median and mode are equal the shape is symmetrical, if these values are different than the shape is not symmetrical.

2) The transform a normal distribution of data into a standard normal distribution.

=> To convert normal distribution data into standard normal distribution we have to convert into :- [ Z - score ]

• we must use the formula :-

[ Z = (X - μ)/σ ]

Here,

* X = data point

* μ = Population mean

* σ = standard deviation

3) The data is transformed to a standard scale called Z-score, that have a mean of '0' and a standard deviation of '1'.

• The values of 'Z' tell us how many standard deviation above (or) below the value is from the mean.

• Here, 1, 2, 3 indicates 1, 2, (or) 3 Standard deviation above the mean and -1, -2, -3 indicates 1, 2, (or) 3 standard deviation below in the mean.

4) The data point represent either X (or) Z.

[ Z = X - mean / Standard deviation ]

• Where, X - data point value

• This is relationship between X and Z.

5) Standard Normal Curve :-

=> If it is because of the symmetrical nature of the curve which has the same nature, above the mean and below the mean.

orchestra answered 1 year ago

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