cadenarenata03
Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.