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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.

Sagot :

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, [tex]\overline T[/tex], given by the combined mean as follows;

[tex]\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 }[/tex]

Where;

[tex]The \ mean \ completion \ time \ for \ each \ step \ is \ \overline x_1 = \overline x_2 = \overline x_3 = 10 \ seconds[/tex]

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

[tex]\overline T = \dfrac{1 \times 10 + 1 \times 10 + 1 \times 10 }{1 + 1 + 1 } = \dfrac{30}{3} = 10 \ seconds[/tex]

Therefore, the mean of T = 10 seconds

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

A normal distribution has two parameters: Mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].

  • For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex].

In this problem, the mean is [tex]\mu = 10[/tex] and the standard deviation is [tex]\sigma = 5[/tex].

For the total completion, there are 3 instances, hence [tex]n = 3, n\mu = 3(10) = 30[/tex], hence, the mean of T is of 30 seconds.

A similar problem is given at https://brainly.com/question/24085252

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