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. A paper described a study in which the left atrial size was measured for a large number of children aged 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.7 mm and a standard deviation of 4.2 mm.

(a) Approximately what proportion of healthy children have left atrial diameters less than 24 mm?

Answer :

Given :

Given Data :

The population mean (μ)=26.7

The population standard deviation (σ)=4.2

Solution :

A) The Proportion of Children with Left Atrial Diameters Less Than 24 mm :

P(x<24)=P(xμσ<2426.74.2) =P(z<0.64) =0.2611

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