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 :

$$\therefore \text{P}(x < 24) = \text{P}\left(\frac{x – \mu}{\sigma} < \frac{24 – 26.7}{4.2}\right) \\$$ $$= \text{P}(z < -0.64) \\$$ $$= 0.2611$$

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