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.

Using the normal distribution, it is found that the mean of T is of 30 seconds.

A normal distribution has two parameters: Mean and standard deviation .

In this problem, the mean is and the standard deviation is .

For the total completion, there are 3 instances, hence , hence, the mean of T is of 30 seconds.

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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;

Where;

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

Therefore, the mean of T = 10 seconds

there are no short passages to look at