2) In a bolt factory,machines M1,M2,M3 manufacture respectively 25,35 and 40 per

ID: 3058506 • Letter: 2

Question

2) In a bolt factory,machines M1,M2,M3 manufacture respectively 25,35 and 40 percent of the total output.Of their output 5,4 and 2 percent respectively are defective bolts.One bolt is drawn at random from the product and is found to be defective. What is the probablity thet it is manufactured in the machinbe M2?

3) If the main printer in a university computer center is oprating properly 90% of the time.Suppose inspections are mde at 10 randomly selected items.

(a) what is the probality that the main printer is operating properly for exactly nine of the inspections?

(b) what is the probality that printer is operating properly in more than 2 inspections?

7) 62% of 12th graders attend school in a particular urban school district.A sample of 50 children are selected.Use normal approximation to find the probability that less than 20 are actually enrolled in school.F(-3,35)=.0004

8) Suppose youare waiting at airport to receive your friend and flight is expected to land in another 20 minutes.By using uniform distribution find the probability that the flight lands in between now and the next 10 minutes?

9) Let the random variable X and Y have joint probability density function

f(x,y)=c(x^2y+xy) ; 0<x<1,0<y<1

(a) Find the value of "c" that makes function a joint density.

(b) Compute E(Y)

10) Let X denote the number of defective gauges and Y denote the number of non defective gauges selected.If the joint density for (X,Y) is given as

Find (a) P(X=2/Y=1)

(B) P(X less than or equal 1,Y greater than or equal 1)

X Y 0 1 2 0 0.03 0.04 0.3 1 0.02 0.09 0.04 2 0.06 0.02 0.4

Explanation / Answer