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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 28E

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I need help solving this problem in R.

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")[https://www.ncbi.nlm.nih.gov/pubmed/19147240] (International Journal of Cardiology [2009]) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, the left atrial diameter was approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm.

i) Use `plotDist` to draw the probability density function of the left atrial diameter.

ii) Generate 50 sample measurements of the left atrial diameters and plot the measurements using a histogram.

iii) Approximately what proportion of healthy children have left atrial diameters less than 23.5 mm?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Building off of the previous questions can you help me solve these?

iv) Approximately what proportion of healthy children have left atrial diameters greater than 32.5 mm?

v) Approximately what proportion of healthy children have left atrial diameters between 24 and 29 mm?

vi) For healthy children, what is the value for which only about 25% have larger left atrial diameter?

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