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The paper referenced in the previous exercise also included data on left atrial diameter for children who were considered overweight. For these children, left atrial diameter was approximately normally distributed with a mean of \(28 \mathrm{~mm}\) and a standard deviation of \(4.7 \mathrm{~mm}\). a. Approximately what proportion of overweight children have left atrial diameters less than \(25 \mathrm{~mm}\) ? b. Approximately what proportion of overweight children have left atrial diameters greater than \(32 \mathrm{~mm} ?\) c. Approximately what proportion of overweight children have left atrial diameters between 25 and \(30 \mathrm{~mm}\) ? d. What proportion of overweight children have left atrial diameters greater than the mean for healthy children?

Consider the variable \(x=\) time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of \(x\) is well approximated by a normal curve with mean 45 minutes and standard deviation 5 minutes. a. If 50 minutes is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted time? b. How much time should be allowed for the exam if you wanted \(90 \%\) of the students taking the test to be able to finish in the allotted time? c. How much time is required for the fastest \(25 \%\) of all students to complete the exam?