Answer :
Final answer:
The Z-score for a class size of 29 students, when the average class size is 39.4 students with a standard deviation of 12.0 students, is approximately -0.87. This score indicates how many standard deviations the value is from the mean.
Explanation:
The Z-score in statistics is a measure by which you can compare a data point to the mean of a group of data. It provides a way to quantify how many standard deviations a data point is from the average. To calculate a Z-score, you subtract the mean from the data point and then divide by the standard deviation.
In your problem, we know that the average class size is 39.4 students and the standard deviation is 12.0 students. You asked for the Z-score for a class with 29 students. We plug these values into our Z-score formula which gives us:
Z = (29 - 39.4) / 12.0 = -0.87 (rounded to two decimal places)
The negative Z-score indicates that this class size of 29 students is below the mean class size of 39.4 students.
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