Question

 

1. In a company production line, the number of defective parts and their probabilities produced in an hour are shown in TABLE 1. Let x be the number of defective parts in an hour and K is P(X=K):

TABLE 1

X	0	1	2	3	4
P(X = x)	0.2	0.3	K	0.15	0.1

1. How many defective parts are expected to be produced in an hour in the company’s production line?                                                                        

      

2. Compute the standard deviation of the defective parts produced in an hour by the company’s production line.                                              

 

3. Find the value of P(0 < X £ 3).                                                                         

 

 

2. Penny will play 2 games of badminton against Monica. Penny’s chances of winning each game is around 60 %. Let X denotes the number of Penny winning the game.
   1. Construct a probability distribution and cumulative probability distribution table for X.

                                                                                                                

2. Graph the probability distribution of X.

Answer 1

value of K = 1-0.2-0.3-0.15-0.1 = 0.25

i)

X	P(X)	X*P(X)	X² * P(X)
0	0.2000	0	0.000
1	0.3000	0.3	0.300
2	0.2500	0.5	1.0000
3	0.1500	0.45	1.3500
4	0.1000	0.4000	1.6000

.

expected defective parts= mean = E[X] = Σx*P(X) =            1.65

ii)

E [ X² ] = ΣX² * P(X) =            4.2500
          
variance = E[ X² ] - (E[ X ])² =            1.5275
          
std dev = √(variance) =            1.2359

iii)

P(0<x<3) = 0.30+0.25 = 0.55

 

2)

X~Bin(2,0.6)

Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

i)

X	P(X)
0	0.1600
1	0.4800
2	0.3600

ii)