A person 's cholesterol level C can be measured by three different tests Test a returns a value Xa with a mean C and a standard deviation 1 2, test returns a value X with a mean C and a standard deviation 2 4 and test returns a value X , with a mean C and a standard deviation 3 1 Suppose that the t...

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A person's cholesterol level C can be measured by three different tests. Test-a returns a value Xa

Question:

A person's cholesterol level C can be measured by three different tests. Test-a returns a value Xa with a mean C and a standard deviation 1.2, test-β returns a value Xβ with a mean C and a standard deviation 2.4. and test-β returns a value X., with a mean C and a standard deviation 3.1. Suppose that the three test results are independent. If a doctor decides to use the weighted average 0.5Xa + 0.3Xβ + 0.2XY what is the standard deviation of the cholesterol level obtained by the doctor?