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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
- a. Approximately what proportion of overweight children have left atrial diameters less than 25 mm?
- b. Approximately what proportion of overweight children have left atrial diameters greater than 32 mm?
- c. Approximately what proportion of overweight children have left atrial diameters between 25 and 30 mm?
- d. What proportion of overweight children has left atrial diameters greater than the mean for healthy children?
7.87. 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 mm and a standard deviation of 4.2 mm.
- a. Approximately what proportion of healthy children have left atrial diameters less than 24 mm?
- b. Approximately what proportion of healthy children have left atrial diameters greater than 32 mm?
- c. Approximately what proportion of healthy children have left atrial diameters between 25 and 30 mm?
- d. For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
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Chapter 7 Solutions
Introduction To Statistics And Data Analysis
- Let X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward
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- 1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill