Engineering College

The production process of rods from machine "A" yields specimen with the following specs. Mean: µ(LA)=20.00mm, STD: s(LA)=0.50mm. You need to purchase new machine to increase the production capacity and accuracy together. If the new machine "B" will produce half of the total rods, what is the STD, s(LB), that needs to achieve the total STD, s(LT)=0.4mm? Assume Corr(A,B)=0.4

Answers

Answer 1

Answer: the standard deviation STD of machine B is s (Lb) = 0.4557

Explanation:

from the given data, machine A and machine B produce half of the rods

Lt = 0.5La + 0.5Lb

so

s² (Lt) = 0.5²s²(La) + 0.5²s²(Lb) + 0.5²(2)Cov (La, Lb)

but Cov (La, Lb) = Corr(La, Lb) s(La) s(Lb) = 0.4s (La) s(Lb)

so we substitute

s²(Lt) = 0.25s² (La) + 0.25s² (Lb) + 0.4s (La) s(Lb)

0.4² = 0.25 (0.5²) + 0.25s² (Lb) + (0.5)0.4(0.5) s(Lb)

0.64 = 0.25 + s²(Lb) + 0.4s(Lb)

s²(Lb) + 0.4s(Lb) - 0.39 = 0

s(Lb) = { -0.4 ± √(0.16 + (4*0.39)) } / 2

s (Lb) = 0.4557

therefore the standard deviation STD of machine B is s (Lb) = 0.4557

Related Questions

Other Questions
2. A line or line segment perpendicular to a line segment at the midpoint of the segment is a... One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 35. Find thelengths of all three sides, to two decimal places.i would appreciate if you showed work so i know how you did it! Whats the answer for 2 1/2,5 3/4 The distance between the two numbers is ANSWER QUICK PLSWhat determines if a biome is a desert?- temperatures - amount of sand- wildlife- precipitation How many moles of calcium are in 5.82g of calcium? Which statement does NOT describe a scientific theory?A)A scientific theory can never be provenB)A scientific theory is supported by facts0)A scientific theory eventually becomes a factD)A scientific theory is a generally accepted explanation If you shift the quadratic parent function, f(x) = x2,right 12 units, what is theequation of the new function?A. g(x) = x + 12B. g(x) = x2 - 12C. g(x) = (x - 12)D. g(x) = (x + 12) Which of the following statement is not true about the Project stakeholders?A. Stakeholders responsibilities may overlap.B. Stakeholders may have different agenda.C. Project Managers must understand how stakeholders can affect the project.D. All stakeholders must be independent of each other. what type of source is this? and why.. What is the purpose of application software policies?a. They define boundaries of what applications are permitted.b. They use a database of signatures to identify malware.c. They take log data and convert it into different formats.d. They serve to help educate users on how to use software more securely The probability that an event will happen is P(E)=34/41.Find the probability that the event will not happen. In A Wrinkle In Time Explain the major conflict , and how was it resolved I will give brainliest!!!! Is the underlined word being used as a helping verb or a main verb? The waves tossed the little boat. Choose 1 answer: (Choice A) A Helping verb (Choice B) B Main verb The area of the football field is 57,600 square feet. If the width of the field is the length,what is the length of the football field? The elements potassium (K) and chlorine (CI) can form an ionic bond. Which of the followingstatements correctly explains what occurs (in this ionic bonding)?1.) As chlorine has 7 valence electrons, it tends to form bonds to gain one electron (to get a full valence shell of 8).On the other hand, potassium has one valence electron, so it tends to lose this electron to other atoms (andbecome a cation)2.) As chlorine has 7 valence electrons, it tends to form bonds to lose all 7 electrons. On the other hand,potassium has one valence electron, so it tends to gain 7 electrons (to get a full valence shell of 8).3.) In this ionic bonding, potassium is the anion and chlorine is the cation.4.) During the ionic bonding between potassium and chlorine, 8 electrons are shared between these 2 atoms. PLZZ HELP!! ITS FOR A TEST!! Third generation computers were set apart because of this invention. A) microprocessors B) transistors C) integrated circuits D) vacuum tubes How do scientific understanding, historical data, and monitoring help scientists predict weather and climate hazards? 3+3 is what type of equation 35. Buddhism and Christianity spread for which of the following reasons? What innovation helped expand the empire and increase trade?