Answer to Question #316315 in Statistics and Probability for vas

Question

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 gearboxe

Answer 1

Let Y=# improperty of drilled gearboxes. Then, Y is hypergeometric with N=20, n=5, r=2

a. 20-2=18 good reductors

P(Y=0)=18/20x17/19x16/18x15/17x14/16=0.553

b. The random variable T, the total time, is given by T=10Y+(5-Y)=9Y+5. Thus,

E(T)=9E(Y)+5=9[5(2/20)]+5=9.5

V(T)=81V(T)=81(0.355)=28.755

$\sigma=5.362$