Respuesta :
The sampling distribution of the difference in sample means x⁻₁ - x⁻₂ is; 3.5 - 3.5 = 0
Difference in sample means
We are told that;
- A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times.
- x⁻₁ represents the average of the first ten rolls.
- x⁻₂ represents the average of the remaining five rolls.
Now, the average of the largest and lowest numbers of the six sided die is;
E(x) = (6 + 1)/2 = 3.5
Thus, the average mean of the first ten rows is expressed as;
E(x⁻₁) = (n * E(x))/n
E(x⁻₁) = (10 * 3.5)/10
E(x⁻₁) = 3.5
The average mean of the last five rolls will be;
E(x⁻₂) = (n * E(x))/n
E(x⁻₂) = (5 * 3.5)/5
E(x⁻₂) = 3.5
Thus;
x⁻₁ - x⁻₂ = 3.5 - 3.5 = 0
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