Explanation Given: The given table is, Country Hong Kong Netherlands U.K. Singapore Switzerland Index 5.70 5.59 5.57 5.56 5.55 Country U.S. Australia Finland Germany Denmark Index 5.55 5.31 5.24 5.23 5.22 Approach: The mean of a random variable X is given by, μ = x 1 p 1 + x 2 p 2 + x 3 p 3 + … + x n p n → ( 1 ) Here, x 1 , x 2 , x 3 , … , x n are values of a random variable X with probabilities p 1 , p 2 , p 3 , … , p n respectively. The variance of a random variable X is given by, Var ( X ) = p 1 ( x 1 − μ ) 2 + p 2 ( x 2 − μ ) 2 + p 3 ( x 3 − μ ) 2 + … + p n ( x n − μ ) 2 → ( 2 ) The standard deviation of a random variable X is given by, σ = Var ( X ) → ( 3 ) Calculation: Assume X denotes the index of a country. The table for the probability distribution of X is shown below. x 5.7 5.59 5.57 5.56 5.55 5.55 5.31 5.24 5.23 5.22 P ( X = x ) 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 Substitute 5.7 for x 1 , 5.59 for x 2 , 5.57 for x 3 , 5.56 for x 4 , 5.55 for x 5 , 5.55 for x 6 , 5.31 for x 7 , 5.24 for x 8 , 5.23 for x 9 , 5.22 for x 10 , 1 10 for p 1 , 1 10 for p 2 , 1 10 for p 3 , 1 10 for p 4 , 1 10 for p 5 , 1 10 for p 6 , 1 10 for p 7 , 1 10 for p 8 , 1 10 for p 9 , and 1 10 for p 10 in formula (1). μ = [ ( 1 10 ) ( 5.7 ) + ( 1 10 ) ( 5.59 ) + ( 1 10 ) ( 5.57 ) + ( 1 10 ) ( 5.56 ) + ( 1 10 ) ( 5

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

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Author: Tan

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Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

Ch. 8.1 - What is a random variable? Give an example.Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Three balls are selected at random without...Ch. 8.1 - 2.A coin is tossed four times. Let the random...Ch. 8.1 - A die is rolled repeatedly until a 6 falls...Ch. 8.1 - Cards are selected one at a time without...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.
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The mean and standard deviation of indices of the top ten nations.

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The mean and standard deviation of indices of the top ten nations.