![samjohnson3637](/avatars/6293.jpg)
samjohnson3637
17.07.2019 •
Mathematics
Afactory worker productivity is normally distributed. one worker produces an average of 75 units per day with a standard deviation of 20. another worker produces at an average rate of 65 per day with a standard deviation of 21. what is the probability that in 1 week (5 working days), worker 1 will outproduce worker 2?
Solved
Show answers
More tips
- P Philosophy Agnosticism: Opinion or Belief?...
- C Computers and Internet How to Calibrate Your Monitor: Useful Tips and Recommendations...
- H Health and Medicine Hangover: How to Get Rid of It Quickly?...
- A Auto and Moto How to Start a Diesel Engine in Cold Weather?...
- A Auto and Moto Which alarm system to choose?...
- P Photography and Videography What is lens calibration and why is it needed?...
- S Science and Technology How to Choose a Picture Frame: Tips and Recommendations...
- P Photography and Videography Understanding HDR: How It Works and Why You Need It...
- P Photography and Videography How to Choose the Perfect Photo Paper for Your Images?...
- C Computers and Internet How to Choose an Uninterruptible Power Supply (UPS) for Your Computer: Expert Tips...
Answers on questions: Mathematics
- M Mathematics Can someone help me? Will mark brainlist if you show work and give the correct answer!...
- M Mathematics Please help answer this for me with full working outs. Thank you.....
- H History The us government may call on its citizens to serve in the military. true or false?...
- M Mathematics Write two algebraic expressions for the area of the algebra tile shown at right. write one expression with parentheses and the other expression without parentheses....
- M Mathematics Chck farms raises hens and roosters. they have enough space to raise at most 300 300 birds per year. each hen eats 80 80 pounds of food per year, and each rooster eats...
Ответ:
Define X = X1 + X2 + X3 + X4 + X5 as the random variable representing the number of units the
first worker produces during the entire week. It is easy to prove that X is normally distributed with mean µx = 5·75 = 375 and standard deviation σx = 20√5.
Similarly, define random variables Y1, Y2,...,Y5 representing the number of units produces by
the second worker during each of the five days and define Y = Y1 + Y2 + Y3 + Y4 + Y5. Again, Y is normally distributed with mean µy = 5·65 = 325 and standard deviation σy = 25√5. Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X −Y > 0). It is a quite surprising fact that the random variable U = X−Y , the difference between X and Y , is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σU, where σ2 U = σ2 x+σ2 y = 400·5+625·5 = 1025·5 = 5125. It follows that σU = √5125. A reference to the above fact can be found online at http://mathworld.wolfram.com/NormalDifferenceDistribution.html.
Now everything reduces to finding P(U > 0) P(U > 0) = P(U −50 √5125 > − 50 √5125)≈ P(Z > −0.69843) ≈ 0.757546 .
Ответ:
idk
Step-by-step explanation: