Question

1. investment earnings an investor calculated these percentages of each of three stock investments with payoffs as shown. find the average payoff. use the weighted mean. stock percent payoff a 30 $10,000 b 50 3,000 c 20 1,000

Explanation:

Step1: Convert percentages to decimals

The formula for weighted mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}w_ix_i}{\sum_{i = 1}^{n}w_i}\). Here, \(w_1 = 0.3\), \(w_2=0.5\), \(w_3 = 0.2\), \(x_1 = 10000\), \(x_2 = 3000\), \(x_3=1000\).

Step2: Calculate the numerator \(\sum_{i = 1}^{n}w_ix_i\)

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Step3: Calculate the denominator \(\sum_{i = 1}^{n}w_i\)

\(\sum_{i = 1}^{n}w_i=0.3 + 0.5+0.2=1\)

Step4: Calculate the weighted mean

\(\bar{x}=\frac{4700}{1}=4700\)

Answer:

\(4700\)