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

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Author: Tan

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Chapter 8.3, Problem 32E

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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.

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To find:

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