The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased The paper “Left Atrial Size Increases with Body Mass Index in Children” (International Journal of Cardiology [2009]: 1–7) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on these data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.4 millimeters and a standard deviation of 4.2 millimeters.
a. Approximately what proportion of healthy children has left atrial diameters less than 24 millimeters?
b. Approximately what proportion of healthy children has left atrial diameters greater than 32 millimeters?
c. Approximately what proportion of healthy children has left atrial diameters between 25 and 30 millimeters?
d. For healthy children, what is the value for which only about 20% have a larger left atrial diameter?