Answer :
On solving the provided question, we can say that standard deviation and mean, The equivalent ACT score is using 1.545 as the z score [tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]
What is standard deviation?
Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
[tex]X = 0.675 * 198 + 1101 = 1235[/tex]
standard deviation and mean
[tex]X = 0.675 * 3.9 + 19.2 = 21.8[/tex]
scores 1407 standardized score z for 1407
[tex]z = (X-μ)/σ = (1407-1101)/198 = 1.545[/tex]
The equivalent ACT score is using 1.545 as the z score
[tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]
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