Statistics

Posted: November 29th, 2013

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Statistics

Chapter 4, 1a

This situation entails a large retail business that employs a hundred sales associates. These associates have been divided to operate in two different groups, the early shift and the late shift. The X factor in this particular situation is the absentee rate for sales associates. This factor can be studied to facilitate the identification of the propensity of absenteeism among the employees. In this case, the result can be able to establish a predictive model that defines the probability of attendance among the employees. This factor can be implemented as a useful predictor that will allow the management to establish the amount of merchandise to purchase and release to the associates at any given period. It will be a good strategy for acquiring the correct amount of products for resale in accordance with the attendance of the employees.

1b

Regarding the number of new businesses started annually in a country, the government of the country in question can consider the rate of business formation every year the X factor. In this case, relevant authorities can be able identify the rate at which business are formed annually in the country and be able to plan ahead. This information can enable the government to put in place significant rules and regulations that govern the starting of businesses in the country. In addition, the government can be able to judge the amount of revenue it would raise from tax every year and formulate a predicted realistic budget

1c

The data collected on the type and severity of injuries at ski resort First Aid stations should be considered the X factor in this situation. The University’s biomechanical engineering department can use this data to identify the type and extent of injuries sustained from skiing related accidents. Hence, this information will be used to design appropriate ski equipment capable of eliminating or reducing the risks involved with the sport.

2a

The producer should in this case consider predicting the sales with regard to where the focus group resides. The appropriate boundary to set in the set prediction should not reflect the interests of the entire target market. The 6-16 aged market is composed of individuals with different values and cultures. Therefore, the scope of the sales prediction should only relate to the focus group rather than the entire target market.

2b

The strawberry farmer should look to consider the two-week meteorological forecasts as well as the climate history of the area. The scope of decision made should extend to both the meteorological forecasts and the climate history of the area.

2c  

The appropriate boundaries and scope of work that the print media publication can consider should revolve around the quantity of the target market and its consumer taste and preference. This should help determine the capacity at which the target market will be willing to purchase.

4a

The estimate of the current transistor count on a computer chip is in 3D design in accordance with the IBM announcement in 2011. Current storage density for a hard disk is estimated at 421 Gbit/in².

4b

The factors have been under constant change and can are expected to be valid as long as other advancements are discovered. Other forms of storage devices or improvements might cause these laws to become obsolete.

4c

According to Moore’s law, the transistor count is subject to change every in every three years, in this case, its capacity doubles. Therefore, in five years, the transistor count can be estimated to be better than the 3D model. According to Kryder’s law, the rate of hard disk storage density change is similar that of the the transistor count. Therefore, the storage density would double to 842 Gbit/in² in five years time.

4d    

Both Moore’s law and Kryder’s law can be used to budget information technology budget needs by predicting the next transistor count or storage density.

Case Study, 1

 

The slope is positive because more sales will rise as more customers are exposed to the ad.

2

 

Case Study, 2

3a

 

 

 

 

 

3b

With increase in advertising time, more sales are made due to increased consumer awareness

3c

37,500 units

3d

If would expect 300 second advertisement time to amount to 49, 600units. I hold no reservations on this prediction

Chapter 5, 1a

The random variable is the waterfowl in the field. The outcome space is the total number of waterfowls divided by sixty (minutes).

1b

The random variable is the strep throat ailment. The outcome space is ½. The test will come out either negative or positive.

1c

The random variable is the vehicles that pass through the tollbooth. The outcome space is the number of vehicles over sixty (minutes)

1d

The random variable is the candy wrapped mints. The outcome space is the incomplete candy pieces over the total candy pieces being counted.

2

Y	P (Y=y)	Average	Variance	Standard deviation
O	0.30	3.2	0.04	2.13
1	0.35	1.41	0.032	1.09
2	0.25	2.45	0.021	1.52
3	0.05	1.03	0.004	0.99
4	0.05	1.01	0.003	0.91

3

Economy	Probability Function p(y)	Return Y  in 1000 $	y*p(y)	(y–Mean[Y])2*p(y)
Recession	0.30	–15	-0.45	0.075
Slow growth	0.40	15	0.2	0.012
Boom	0.30	30	9	2.7
SUM	1.0	n.a.	Mean[Y]=	V[Y]= SD[Y]=

 

 

 

 

 

4a

Pr (Y = u) = 1

4b

Fy (y) = P(Y≤y)

4c

3/ Pr (Y = u) = 1

7a

	Average	Variance	Covariance
Returns from bank stock	4.7	0.12	2.52
Returns from health care stock	1.41	0.518	3.51

7b

The expected returns and risk of each of the individual stocks are;

Returns from bank stock- 12.5 return on stock and 3.52% risk

Returns from health care stock- 9.32 return on stock and 1.57% risk

7c

Indeed, the returns of the two stocks are dependent. I arrived at my answer on the premise that most investors do isolate the stock they have held. Instead, they opt to secure a portfolio of combined stocks.

7d

Returns from bank stock- 5%

Returns from health care stock- 9.1%

Standard deviation:

Case Study

Returns from Woodside corporation- 11%

Returns from Brookside corporation- 13.1%

Chapter 6, 1a

The demand of the stock is the outcome space. It is discrete.

1b

The amount of money market fund is the outcome space. It is discrete

1c

The outcome space is the speed of the winner. It is discrete

1d

The outcome space is the total number particulates to be counted. It is continuous

1e

The outcome space is the total weight gained. It is continuous.

2a

1800/1500 X 210 = 420

2b

1600/1500 X 210 = 224

2c

1500/1500 X 210 = 210

2d

1500/1400 X 210 = 225

2e

1500/1200 X 210 = 252.5

3a

Z= 0.365

3b

Z= 0.541

3c

Z= 0.625

3d

Z= 0.305

3e

Z= 0.481

Z= 0.874

3f

Z= 0.397

3g

Z= 1.004

3h

Z= 0.547

3i

Z= 0.472

3j

Z= 0.021

4a

3150 – 2900= 250

200 X 250/3050 = 0.1693

4b

4200$

4c

0.245

5a

2 hours

5b

5 hours

5c

10 hours

5d

15 hours

5e

18 hours

6a

0.684

6b

$13,375

6c

0.215

9a

13

9b

25

9c

30

9d

45

9e

30

9f

69

9g

360

Case study, 1

Machine 1- 4.15

Machine 2 -9.31

Machine 3-6.21

2

0.05 + 0.10 + 0.25 = 0.4

3

The system reliability would rise by 0.6

4

0.55

5

0.05 + 0.10 = 0.15