Step 1 :Given values are the mean of 7.5, standard deviation of 1.4, margin of error of 0.06, and z-score of 2.576.
Step 2 :We need to find the minimum sample size required to create the specified confidence interval.
Step 3 :The formula to calculate the sample size is \((z \cdot \sigma / E)^2\), where \(z\) is the z-score, \(\sigma\) is the standard deviation, and \(E\) is the margin of error.
Step 4 :Substitute the given values into the formula: \((2.576 \cdot 1.4 / 0.06)^2\).
Step 5 :Calculate the value to get the sample size, and round up to the next integer.
Step 6 :The minimum sample size required to create the specified confidence interval is \(\boxed{3613}\).