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Sagot :
The standard deviation is decreases then the graph of the normal z - score curve is increases.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.
In mathematics, the Z score is used to quantify how many standard deviations the raw score deviates from or approaches the mean. Giving the z score are:
z = (x - μ ) / σ
Where,
x = raw score
μ = mean
σ = standard deviation
For a sample size,
z = (x - μ ) / σ / [tex]\sqrt{n}[/tex]
The z score affects the area under the curve. The area under the curve increases as the z score increases and decreases as the z score decreases.
The standard deviation has an inverse relationship with the area under the curve (z score). The z score drops as the standard deviation rises, diminishing the area under the curve.
The area under the curve grows as the standard deviation is reduced because the z score increases.
Therefore,
The standard deviation is decreases then the graph of the normal z - score curve is increases.
To learn more about Standard deviation visit :
brainly.com/question/23907081
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