Question

A factory process requires 3 steps to finish a product. The steps each have a mean completion time of μ=10 seconds and a standard deviation of σ=5 seconds. The time it takes to complete each step is independent from the other steps. Let T be the total completion time of the 3 steps on a randomly chosen product.
Find the mean of T.

Answer 1

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, $\overline T$, given by the combined mean as follows;

$\overline T = \dfrac{n_1 \cdot \overline x_1 + n_2 \cdot \overline x_2 + n_3 \cdot \overline x_3 }{n_1 + n_2 + n_3 }$

Where;

$The \ mean \ completion \ time \ for \ each \ step \ is \ \overline x_1 = \overline x_2 = \overline x_3 = 10 \ seconds$

n₁ = n₂ = n₃ = 1, each step is taken only once, we have;

$\overline T = \dfrac{1 \times 10 + 1 \times 10 + 1 \times 10 }{1 + 1 + 1 } = \dfrac{30}{3} = 10 \ seconds$

Therefore, the mean of T = 10 seconds

Answer 2

Answer:

30

Step-by-step explanation:

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