Qt - Assignment Week 1
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Possion distribution table for this example Question :
Poisson Distribution
a.
6 customer / 4 min
Answer
0.0407
b. Answer c. 1
4.07%
0 customers / 4 min. 0.0608
6.08%
teller can not serve no more than 4 customers / 4 min. probability of teller will not be able to meet the demand 1 - .1557 - 0.2225 - 0.2384 - 0.1703 - 0.0608
Answer 2 Answer 3
0.1523
15.23%
Input = Customer 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Tailor will be able to meet the demand 0.8477
84.77%
What % of time second window have to be opended?
Answer 15.23% of the time d 1 Answer
2
Exactly 3 people will arrive in 2 mi. interval 0.1128
11%
5 or more customers in 8 min. period 1 - 0.0037 - 0.0207 - 0.0580 - 0.1082 - 0.1515
Answer
Input = Input ( for this problem) = Customer 0 1 2 3 4
0.6579
66%
Input = Input ( for this problem) = Customer 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23
ution table for this example λ = 2.8 / 4 min. Probability 0.0608 0.1703 0.2384 0.2225 0.1557 0.0872 0.0407 0.0163 0.0057 0.0018 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000
% Probability 6.08% 17.03% 23.84% 22.25% 15.57% 8.72% 4.07% 1.63% 0.57% 0.18% 0.05% 0.01% 0.00% 0.00% 0.00% 0.00%
λ = 2.8 / 4 min. λ = 1.4 / 2 min. Probability 0.2466 0.3452 0.2417 0.1128 0.0395
% Probability 24.66% 34.52% 24.17% 11.28% 3.95%
λ = 2.8 / 4 min. λ = 5.6 / 8 min. Probability 0.0037 0.0207 0.0580 0.1082 0.1515 0.1697 0.1584 0.1267 0.0887 0.0552 0.0309
% Probability 0.37% 2.07% 5.80% 10.82% 15.15% 16.97% 15.84% 12.67% 8.87% 5.52% 3.09%
0.0157 0.0073 0.0032 0.0013 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.57% 0.73% 0.32% 0.13% 0.05% 0.02% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Question :
Binomial Distribution
a.
exactly 14 buyers will use internet for pricing info.
Answer
b. Answer c. Answer
0.14
14%
Input 78% 75% 70% Random 20 samples
All the buyers will use unternet to send PO 0
0.3%
Fewer than 12 will use internet for PO acknowledgement 0.1133
11.3%
total buyers = 20 Probabiltiy = 0.7 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
n
will use for pricing information will use to send POs will use for PO acknolwedgement Random 20 samples
total buyers = 20 Probabiltiy = 0.7 table 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0039 0.0120 0.0308 0.0654 0.1144 0.1643 0.1916 0.1789 0.1304 0.0716 0.0278 0.0068 0.0008
p 20 20 20
x 0.78 0.74 0.7 < 12
14 20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0041 0.0132 0.0351 0.0765 0.1356 0.1923 0.2131 0.1777 0.1050 0.0392 0.0069
Question : a.
Normal Distribution Cell phone bill > 67.75 z= =
( 67.75 - 42.78) / 11.35 2.2
Probability =
0.49
Probability of bill > 67.75 = 0.5 - 0.4861 Answer b.
=
0.01
phone bill is between 30 & 50 probability for > 50 bill z= ( 50 - 42.78) / 11.35 = 0.64
probability for < 30 bill z= ( 30 - 42.78) / 11.35 = -1.13
Probability =
Probability =
0.24
Probability of bill between 30 & 50 = 0.2389 + 0.3708 = Answer c.
=
0.37 0.61
0.76
Phone bill is < than 25 z= =
( 25 - 42.78) / 11.35 -1.57
Probability =
0.44
Probability of bill < 25 = 0.5 - 0.4418 Answer d.
=
0.06
phone bill is between 45 & 55 probability for > 45 bill z= ( 45 - 42.78) / 11.35 = 0.20
probability for > 55 bill z= ( 55 - 42.78) / 11.35 = 1.08
Probability =
Probability =
0.08
Probability of bill between 45 & 55 = 0.3599 - 0.0793 = Answer
=
0.28
0.36
Input Mean = 42.78 Std. deviation = 11.35
Question :
Normal Distribution Input Mean = 30000 Std. deviation = 9000
a.
what portion of the cost are between 15000 & 45000? For 30000 till 45000 z= ( 45000 - 30000) /9000 = 1.67
For 15000 till 30000 z= ( 15000 - 30000) / 9000 = -1.67
Probability =
Probability =
0.45
Probability = 0.4525 + 0.4525 = Answer = b.
0.45
0.91
0.91
what portion of the cost are > 50000? For cost > 50000 z= ( 50000 - 30000) /9000 = 2.22 Probability =
0.49
Probability of cost > 50000 = 0.5 - 0.4868 = Answer = c.
0.01
0.01
what proportion of the cost is between 5000 & 20000? For 30000 till 20000 z= ( 20000 - 30000) /9000 = -1.11
For 5000 till 20000 z= ( 5000 - 30000) /9000 = -2.78
Probability =
Probability =
0.37
Probability of the cost between 5000 & 20000 = 0.4973 - 0.3665 Answer = d.
0.13
90.82% of the cost are more than 7000, what is standard deviation? Input Mean = 30,000 Probability = 90.82 - 50 = 40.82 Z value = 1.33 ( in the table value corresponds to 0.4082) Std deviation = ( 7000-30000)/1.33 -17293.23 Value is negative since it is on the left side of the center
0.5
Answer = e.
17293.2
79.95 % cost were less than 33000, what's mean? Input Standard deviation = 9000 Probability = 79.95 - 50 = 29.95 Z value = 0.84 ( in the table value corresponds to 0.2995) Mean = ( 33000 - ( 9000*0.84) 25440 Value is negative since it is on the left side of the center
Answer =
25440
Mean = 30000 Std. deviation = 9000
Poisson Distribution
a.
6 customer / 4 min
Answer
0.0407
b. Answer c. 1
4.07%
0 customers / 4 min. 0.0608
6.08%
teller can not serve no more than 4 customers / 4 min. probability of teller will not be able to meet the demand 1 - .1557 - 0.2225 - 0.2384 - 0.1703 - 0.0608
Answer 2 Answer 3
0.1523
15.23%
Input = Customer 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Tailor will be able to meet the demand 0.8477
84.77%
What % of time second window have to be opended?
Answer 15.23% of the time d 1 Answer
2
Exactly 3 people will arrive in 2 mi. interval 0.1128
11%
5 or more customers in 8 min. period 1 - 0.0037 - 0.0207 - 0.0580 - 0.1082 - 0.1515
Answer
Input = Input ( for this problem) = Customer 0 1 2 3 4
0.6579
66%
Input = Input ( for this problem) = Customer 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23
ution table for this example λ = 2.8 / 4 min. Probability 0.0608 0.1703 0.2384 0.2225 0.1557 0.0872 0.0407 0.0163 0.0057 0.0018 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000
% Probability 6.08% 17.03% 23.84% 22.25% 15.57% 8.72% 4.07% 1.63% 0.57% 0.18% 0.05% 0.01% 0.00% 0.00% 0.00% 0.00%
λ = 2.8 / 4 min. λ = 1.4 / 2 min. Probability 0.2466 0.3452 0.2417 0.1128 0.0395
% Probability 24.66% 34.52% 24.17% 11.28% 3.95%
λ = 2.8 / 4 min. λ = 5.6 / 8 min. Probability 0.0037 0.0207 0.0580 0.1082 0.1515 0.1697 0.1584 0.1267 0.0887 0.0552 0.0309
% Probability 0.37% 2.07% 5.80% 10.82% 15.15% 16.97% 15.84% 12.67% 8.87% 5.52% 3.09%
0.0157 0.0073 0.0032 0.0013 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.57% 0.73% 0.32% 0.13% 0.05% 0.02% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Question :
Binomial Distribution
a.
exactly 14 buyers will use internet for pricing info.
Answer
b. Answer c. Answer
0.14
14%
Input 78% 75% 70% Random 20 samples
All the buyers will use unternet to send PO 0
0.3%
Fewer than 12 will use internet for PO acknowledgement 0.1133
11.3%
total buyers = 20 Probabiltiy = 0.7 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
n
will use for pricing information will use to send POs will use for PO acknolwedgement Random 20 samples
total buyers = 20 Probabiltiy = 0.7 table 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0039 0.0120 0.0308 0.0654 0.1144 0.1643 0.1916 0.1789 0.1304 0.0716 0.0278 0.0068 0.0008
p 20 20 20
x 0.78 0.74 0.7 < 12
14 20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0041 0.0132 0.0351 0.0765 0.1356 0.1923 0.2131 0.1777 0.1050 0.0392 0.0069
Question : a.
Normal Distribution Cell phone bill > 67.75 z= =
( 67.75 - 42.78) / 11.35 2.2
Probability =
0.49
Probability of bill > 67.75 = 0.5 - 0.4861 Answer b.
=
0.01
phone bill is between 30 & 50 probability for > 50 bill z= ( 50 - 42.78) / 11.35 = 0.64
probability for < 30 bill z= ( 30 - 42.78) / 11.35 = -1.13
Probability =
Probability =
0.24
Probability of bill between 30 & 50 = 0.2389 + 0.3708 = Answer c.
=
0.37 0.61
0.76
Phone bill is < than 25 z= =
( 25 - 42.78) / 11.35 -1.57
Probability =
0.44
Probability of bill < 25 = 0.5 - 0.4418 Answer d.
=
0.06
phone bill is between 45 & 55 probability for > 45 bill z= ( 45 - 42.78) / 11.35 = 0.20
probability for > 55 bill z= ( 55 - 42.78) / 11.35 = 1.08
Probability =
Probability =
0.08
Probability of bill between 45 & 55 = 0.3599 - 0.0793 = Answer
=
0.28
0.36
Input Mean = 42.78 Std. deviation = 11.35
Question :
Normal Distribution Input Mean = 30000 Std. deviation = 9000
a.
what portion of the cost are between 15000 & 45000? For 30000 till 45000 z= ( 45000 - 30000) /9000 = 1.67
For 15000 till 30000 z= ( 15000 - 30000) / 9000 = -1.67
Probability =
Probability =
0.45
Probability = 0.4525 + 0.4525 = Answer = b.
0.45
0.91
0.91
what portion of the cost are > 50000? For cost > 50000 z= ( 50000 - 30000) /9000 = 2.22 Probability =
0.49
Probability of cost > 50000 = 0.5 - 0.4868 = Answer = c.
0.01
0.01
what proportion of the cost is between 5000 & 20000? For 30000 till 20000 z= ( 20000 - 30000) /9000 = -1.11
For 5000 till 20000 z= ( 5000 - 30000) /9000 = -2.78
Probability =
Probability =
0.37
Probability of the cost between 5000 & 20000 = 0.4973 - 0.3665 Answer = d.
0.13
90.82% of the cost are more than 7000, what is standard deviation? Input Mean = 30,000 Probability = 90.82 - 50 = 40.82 Z value = 1.33 ( in the table value corresponds to 0.4082) Std deviation = ( 7000-30000)/1.33 -17293.23 Value is negative since it is on the left side of the center
0.5
Answer = e.
17293.2
79.95 % cost were less than 33000, what's mean? Input Standard deviation = 9000 Probability = 79.95 - 50 = 29.95 Z value = 0.84 ( in the table value corresponds to 0.2995) Mean = ( 33000 - ( 9000*0.84) 25440 Value is negative since it is on the left side of the center
Answer =
25440
Mean = 30000 Std. deviation = 9000
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