Question

4) Make the following binomial table, where column x =0,1,2,3,4,5. And p(x) is the probability of each event

X	P(X)	x*p(x)	Ex2 * p(x)
0	.395	0	0
1	.093	.093	.093
2	.023	.046	.092
3	.023	.069	.207
4	.070	.28	1.12
5	.140	.7	3.5
6	.070	.42	2.52
7	.093	.651	4.557
8	.093	.744	5.952
Total	.999	3.003	18.041

5) Complete a probability histogram of the date above using the x and p(x) column.

6) Complete the following questions:

a) What is the probability that none of the product is from your company?  

b) What is the probability that more than one product is from your company?

c) What is the probability that at least three products are from your company?

d) What is the probability that at most two products are from your company?

e) What is the probability that all of the 5 products are from your company? ________

f) What is the average number of products from your company? ____________

g) Using the range rule of thumb for usual values, what are the lowest and highest number of products you would expect to pick?

Answer 1

5)

6)

a) 0.395

b) 0.512

c)

P(X>=3) =

0.489

d)

= P(X<=2)

= 0.511

e)

=0.14

f)

X	P(X)	X*P(X)
0	0.40	0.000
1	0.09	0.093
2	0.02	0.046
3	0.02	0.069
4	0.07	0.280
5	0.14	0.700
6	0.0700	0.420
7	0.0930	0.65
8	0.0930	0.7440

mean = E[X] = Σx*P(X) =            3

g)

X	P(X)	X*P(X)	X² * P(X)
0	0.40	0.000	0.000
1	0.09	0.093	0.093
2	0.02	0.046	0.092
3	0.02	0.069	0.207
4	0.07	0.280	1.120
5	0.14	0.700	3.500
6	0.0700	0.420	2.520
7	0.0930	0.65	4.56
8	0.0930	0.7440	5.9520

mean = E[X] = Σx*P(X) =            3
          
E [ X² ] = ΣX² * P(X) =            18.0410
          
variance = E[ X² ] - (E[ X ])² =            9.0230
          
std dev = √(variance) =            3

Range = 4 * S.D

= 12

Thanks in advance!

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