Answer:
The mean of T is 10 seconds
Step-by-step explanation:
The given parameters are;
The mean completion time of each step, μ = 10 seconds
The standard deviation, σ = 5 seconds
Each step is independent from the other steps
The variable that represents the total completion time for the three steps = T
We have the mean of T,
, given by the combined mean as follows;
![\overline T = \dfrac{n_1 \cdot \overline x_1 + n_2 \cdot \overline x_2 + n_3 \cdot \overline x_3 }{n_1 + n_2 + n_3 }](https://tex.z-dn.net/?f=%5Coverline%20T%20%3D%20%5Cdfrac%7Bn_1%20%5Ccdot%20%5Coverline%20x_1%20%2B%20n_2%20%5Ccdot%20%5Coverline%20x_2%20%2B%20n_3%20%5Ccdot%20%5Coverline%20x_3%20%7D%7Bn_1%20%2B%20n_2%20%2B%20n_3%20%7D)
Where;
![The \ mean \ completion \ time \ for \ each \ step \ is \ \overline x_1 = \overline x_2 = \overline x_3 = 10 \ seconds](https://tex.z-dn.net/?f=The%20%5C%20mean%20%5C%20completion%20%5C%20time%20%5C%20for%20%5C%20each%20%5C%20step%20%5C%20is%20%5C%20%20%20%5Coverline%20x_1%20%3D%20%5Coverline%20x_2%20%3D%20%5Coverline%20x_3%20%3D%2010%20%5C%20seconds)
n₁ = n₂ = n₃ = 1, each step is taken only once, we have;
![\overline T = \dfrac{1 \times 10 + 1 \times 10 + 1 \times 10 }{1 + 1 + 1 } = \dfrac{30}{3} = 10 \ seconds](https://tex.z-dn.net/?f=%5Coverline%20T%20%3D%20%5Cdfrac%7B1%20%5Ctimes%2010%20%2B%201%20%5Ctimes%2010%20%2B%201%20%5Ctimes%2010%20%7D%7B1%20%2B%201%20%2B%201%20%7D%20%3D%20%5Cdfrac%7B30%7D%7B3%7D%20%20%3D%2010%20%5C%20seconds)
Therefore, the mean of T = 10 seconds