Statistics Problems

12.1

Random Numbers
													Observed Data		Uniform Assumption			Chi-Square Calculations
The RAND function was used but pasted as values to avoid recalculation													Bin	Frequency	Cumulative Probability	Bin Probability	Expected Frequency	(Observed - Expected)^2/Expected
											Bin		0.1	13	0.100	0.100	10.000	0.9000
0.5514251409	0.9317998354	0.1972196623	0.607028108	0.0019459038	0.8010993156	0.7321547284	0.0387667372	0.6125340901	0.4783007796		0		0.2	16	0.200	0.100	10.000	3.6000
0.1534818867	0.7887652933	0.7259291751	0.4723037784	0.0192327317	0.1765744629	0.3205772071	0.6568298731	0.976823832	0.9561750747		0.1		0.3	10	0.300	0.100	10.000	0.0000
0.2807086225	0.2731009467	0.1131179202	0.9884432105	0.7663278105	0.1813799849	0.9625347011	0.0402243745	0.2864621185	0.8033668602		0.2		0.4	8	0.400	0.100	10.000	0.4000
0.0920302025	0.0225023845	0.1067310442	0.2995186393	0.4944578417	0.1782028618	0.0342107351	0.5126464287	0.4600296783	0.8720953017		0.3		0.5	11	0.500	0.100	10.000	0.1000
0.1758683253	0.6454830218	0.4330017655	0.3839046313	0.5320624112	0.3564923978	0.8494069138	0.4466346717	0.3816807749	0.4414431092		0.4		0.6	10	0.600	0.100	10.000	0.0000
0.5777529554	0.3122071544	0.4219271314	0.3952530165	0.6166458565	0.0936650653	0.7165897897	0.4271807561	0.4483771093	0.2444521949		0.5		0.7	10	0.700	0.100	10.000	0.0000
0.1436993236	0.6022452758	0.6537676304	0.7757871837	0.1585159415	0.8934849576	0.2113231335	0.0852291782	0.5540736642	0.6119166155		0.6		0.8	7	0.800	0.100	10.000	0.9000
0.8331879401	0.1250379357	0.3574497024	0.8468769065	0.1129243286	0.7616702855	0.9019045415	0.1285408459	0.1285297865	0.9192752286		0.7		0.9	7	0.900	0.100	10.000	0.9000
0.1079433795	0.6572167638	0.5573384549	0.5207388248	0.0979095501	0.3827235151	0.5198541239	0.1091035777	0.5712398989	0.2798295991		0.8		1	8	1.000	0.100	10.000	0.4000
0.2490129278	0.2026845486	0.4138390009	0.2437855382	0.0993567401	0.9399452457	0.6491498937	0.0136807829	0.5448718183	0.0986054094		0.9
											1						Chi Squared Statistic	7.2000
Bin	Frequency																Degrees of freedom	9
0	0																Critical value	16.919
0.1	13
0.2	16														Since the Chi Squared statistic < Critical value, do not reject hypothesis of uniformity
0.3	10
0.4	8
0.5	11
0.6	10
0.7	10
0.8	7
0.9	7
1	8
More	0

Random Numbers

Frequency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 More 0 13 16 10 8 11 10 10 7 7 8 0

Bin

Frequency

12.2

Customer Sampling Using Random Number Generation Tool
8		Min	1		Count	Frequency
7		Max	13		1	3
6					2	2
8					3	2
7					4	11
9					5	12
8					6	12
7					7	21
8					8	13
6					9	8
8					10	8
9					11	2
8					12	4
11					13	2
7
8					82%	of the days there will be at least 5 customers
4
5
6
13
3
7
9
5
9
5
6
7
9
5
4
10
4
6
4
10
9
6
5
6
7
7
5
3
8
12
7
4
10
1
7
10
4
4
6
5
6
7
6
10
9
12
5
4
7
7
10
8
6
4
7
1
12
7
2
5
2
10
7
10
7
1
7
5
7
12
7
4
4
6
7
9
5
5
8
8
11
8
13
8

12.3

Weekly Demand
Demand, x	Probability, f(x)	Cumulative probablity		Random Number Interval		Demand
0	0.2	0.2
1	0.4	0.6
2	0.3	0.9
3	0.1	1
4 or more	0
Random variates
Sample	Random number	Demand

12.6

GMAT Scores
Mean	620
Standard deviation	15
Random Variates
Sample	Score

12.18

Stock Prices
			Day	Price
Current Price	$53.00
Mean	$0.003227
S.D.	$0.026154

Daily Price Changes

Price