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In an assembly-line production of industrial robots,
Chapter 3, Problem 117E(choose chapter or problem)
Problem 117E
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty gearboxes are in stock, 2 with improperly drilled holes. Five gearboxes must be selected from the 20 that are available for installation in the next five robots.
a Find the probability that all 5 gearboxes will fit properly.
b Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
Questions & Answers
QUESTION:
Problem 117E
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty gearboxes are in stock, 2 with improperly drilled holes. Five gearboxes must be selected from the 20 that are available for installation in the next five robots.
a Find the probability that all 5 gearboxes will fit properly.
b Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
ANSWER:
Solution
Step 1of 2
a) We have to find the probability of all 5 fit properly
Let X is improperly drilled boxes
Here N=20
n=5
r= improperly drilled holes=2
The pmf of hyper geometric distribution is
All 5 should fit properly means none of them fit improperly
That is
=
=1(8568)/15504
=0.553
Hence the probability of all 5 fit properly is 0.553