Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

The amount of time needed for a certain machine to process a job is a random variable with mean EXi = 10 minutes and Var(Xi)=2 minutes2. The times needed for different jobs are independent from each other. Find the probability that the machine processes less than or equal to 40jobs in 7hours.

Sagot :

fichoh

Answer:

0.98732

Step-by-step explanation:

Given that :

Mean = 10 minutes

Variance = 2 minutes

For less than equal 40 jobs

Mean (m) = 40 * 10 = 400 minutes

Variance = 2 * 40 = 80 minutes

Standard deviation (s) = √variance = √80

Converting hours to minutes

X = 60 * 7 = 420 minutes

P(X≤ 420) :

Z = (x - m) / s

P(X≤ 420) :

Z = (420 - 400) / √80

Z = 20 / √80 = 20 / 8.9442 = 2.236

P(Z ≤ 2.236) = 0.98732

The probability that the machine processes less than or equal should be 0.98732

Calculation of the probability:

Since

Mean = 10 minutes

Variance = 2 minutes

For less than equal 40 jobs

Mean (m) = 40 ( 10) = 400 minutes

Variance = 2 (40) = 80 minutes

Now

Standard deviation (s) = √variance = √80

Now here we Converting hours to minutes

So,

X = 60 (7) = 420 minutes

Now

P(X≤ 420) :

Z = (x - m) / s

Z = (420 - 400) / √80

Z = 20 / √80

= 20 / 8.9442

= 2.236

Now finally

P(Z ≤ 2.236)

= 0.98732

Hence, The probability that the machine processes less than or equal should be 0.98732

Learn more about probability here: https://brainly.com/question/3066522

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.