ADMS 2320 Lecture Notes - Lecture 5: Normal Distribution, Probability Distribution, Standard Deviation

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violetmuskrat777

15 Sep 2016

School

York University

Department

Administrative Studies

Course

ADMS 2320

Professor

Nursel Ruzgar

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Document Summary

Uncountable number of values and it may have an end and may have a beginning. You can"t find an exact probability like p(x=5) = 0. The value can keep dividing an go onto infinity. Has to be told that the distribution is uniform. *have to separate problem from the questions* a will be lower limit and b will be your upper limit in the problem. X1 and x2 comes from the question; x2 is the upper limit and x1 is the lower limit. Cut the normal in the centre, the value is 0 and this is where the mean lies. The tails never touch x-axis because it goes into positive and negative infinity. Sum of entire distribution should equal to 1. Standard deviation affects the shape of f(x) by the middle peak starts to flatten and it has a direct impact on the shape.

Related Questions

1. In its standardized form, the normal distribution

(a) has a mean of 0 and a standard deviation of 1.

(b) has a mean of 1 and a variance of 0.

(d) cannot be used to approximate discrete probability distributions.

2. For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770.

The value of Z is

(a) 0.18

(b) 0.81

(d) 1.47

3. For some value of z, the probability that a standard normal variable is below z is 0.2090. The value of Z is

(a) -0.81

(b) -0.31

(d) 1.96

4. For some positive value of X, the probability that a standard normal variable is between 0 and +2x is 0.1255.

The value of X is

(a) 0.99

(b) 0.40

(d) 0.16

5. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 35. minutes and a standard deviation of minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

(a) 0.3551

(b) 0.3085

(d) 0.1915

corallouse410

Case study : Protecting the public ( Engineering Economy )

The Greenacres City Council has just been informed that the city park may have had a lowgrade contaminant included with the latest annual mosquito spraying. The cityâs health department has been assigned the task of testing for the contaminant and quantifying the health impact of exposure if the contaminant is present. Even though the department cannot yet quantify the effects, they have identified the causal chain for the health problems. The key link here is burning of contaminated vegetation, which puts the contaminant back in the air as a vapor. This vapor is irritating to the eyes and may cause acute damage to people wearing contact lenses. This is substantial evidence that there is no problem if it is touched or even eaten. Thus the chief danger appears to be campfires, disposal of windblown leaves (which would mix in with local residential area), or the chance of wildfire in the park. The health department has also verified that sunshine reduces the toxicity for the potential contaminant over a 2 to 3 year period. By year 4 the danger should be gone. Because of the adverse publicity that the council expects, it has decided that a benefit/cost analysis must be conducted immediatelyâbefore the health department can supply any results. In fact, their meeting is tomorrow night, and you (the cityâs manager) have been ordered to have preliminary results by then. While they would like to have definitive conclusions, you believe that they will settle for an analysis that quantifies the two worst-case scenarios. One scenario involves removing all

vegetation and turning the park into a landfill, while the second scenario involves the maximum health cost in the complete absence of recovery efforts. The city engineer has dragged together the estimates for the landfill scenario. Here the first step is to remove the vegetation and burn it in a specially controlled environment where the exhaust is passed through a catalyst. Fortunately, the city is in an industrial area, so that facilities for disposal of hazardous wastes are available. If these facilities were not close by, then costs would be even higher than the expected $2 million to $5 million. The second step is to create a substantial cover by using the site as a temporary landfill. Fortunately, water table and location factors are positive, except that 20 homeowners will have to be bought out through eminent domain. The appraised value of their properties averages $135,400. The city engineer suggests that all of the other costs associated with using this as a landfill can be ignored, since the city would be incurring them at another site in any case. In about three years the cover would be deep enough and the landfill could be converted back into a park. The park currently emphasizes vegetation, jogging paths, and similar natural uses, but plantings and regrowth are likely to be far too slow. Thus the engineer has suggested using the area for a complex of playing fields for softball, baseball, soccer, and football. This would cut the regrowth time to the minimum and would only require $300,000 for construction. The planner for the city park department has looked at usage levels for other playing fields within the city, and has used benefit numbers developed for justification of another small group of playing fields last year. From this she has suggested that the playing field complex would have a ânet benefitâ stream of $125,000 annually after maintenance costs are considered. She also identified 5% as the discount rate that the city council accepted for that study. The scenario for health impacts if there is no recovery effort is far less defined. Here the difficulty lies in estimating the probability of different kinds of fires, and then estimating how many people might be affected. A wildfire is clearly the least likely; but it could affect the 35,000 people who live in moderate proximity to the park. The fire chief has estimated the normal wildfire possibility at .002, but this may increase to .01 due to publicity and arson. On the other hand, over a 3-year period, someone is almost certain to build a fire with a stick that has been sprayed. Over 20% of the parkâs visitors are picnickers, and a quarter use wood, not charcoal fires. This yearâs leaves are less of a problem, although taking all leaves to the special incinerator is likely to cost nearly $1 million (from close-by neighborhoods, as well as the park).
Cases in Engineering Economy 2nd by Peterson & Eschenbach

It is clear that, if the contaminant is there and if you burn it under your hamburger, there is still a sizable chance that you will have absolutely no problem. But, the exact danger is not known. It appears likely that the cumulative danger is related to park usage, which is currently 250,000 visitor-hours per yearâgrowing at about 15,000 hours per year, slightly faster than the cityâs population. You know that other uncertainties include the study period and the value of avoiding eye damage. Clearly, an exact answer is impossible. Nevertheless, an answer is required.

Suggestions to the Student 1. For the landfill/sports complex option, is it appropriate to include the benefits of the later years?

2. What study period, fraction of population with contacts, etc., must be guesstimated?

3. The role of population growth is likely to matter only for park usage, and not for potential eye damage. Why?

4. What other options should be suggested, based on the economic analysis? Which pieces of the two options have particularly good or poor benefit/cost impacts?

I need answer for this questions :

1) Case Study Description (it must be one page)

2) Case Study Questions .

3 ) Case Study Financials

Question 1

Which of the following approaches to understanding and predicting consumer behavior depends primarily on the knowledge and experience of a firm's employees and its suppliers?

		Test marketing and price experiments
		Analysis of historical data.
		Direct consumer surveys.
		Expert opinion.

Question 2

In which of the following situations would reliance on expert opinion as a basis for a managerial decision be most preferred?

		When the product being marketed is relatively new.
		When the level of economic activity can have a significant effect on the demand for the firm's output.
		When the product can be packaged with a variety of price and quality combinations.
		When the business in question serves as a supplier of inputs to other businesses, especially in multi-product situations where other strategies may be prohibitively expensive.

Question 3

The approach to analyzing consumer behavior that asks consumers to rank and choose among different product attributes to reveal their relative valuation of different characteristics is called:

		conjoint analysis.
		contingent valuation.
		the hedonic estimation technique.
		a direct consumer survey.

Question 4

All of the following are limitations of direct consumer surveys except:

		the possibility of response biases because survey respondents may not want to reveal their true preferences.
		the possibility that the type of questions asked may unintentionally bias the respondent's answers.
		the likelihood that respondents will deliberately and systematically mislead interviewers.
		the possibility that consumers' responses may not reflect their actual behavior in the market place.

Question 5

Which of the following approaches to understanding and predicting consumer behavior does not actually solicit any information from potential customers?

		Expert opinion.
		Test marketing.
		Analysis of historical data.
		Conjoint analysis.

Question 6

Data collected on a sample of individuals with different characteristics at a specific point in time are called:

		panel data.
		cross-section data.
		time series data.
		none of the above.

Question 7

Which of the following approaches to understanding and predicting consumer behavior provides the most insight into how consumers can be expected to respond in an actual market setting?

		Test marketing.
		Conjoint analysis.
		Expert opinion.
		Analysis of historical data.

Question 8

An approach to analyzing consumer behavior in which consumer reaction to different prices is analyzed in a laboratory situation or a test market is called:

		non-price experiments.
		focus groups.
		price experiments.
		none of the above.

Question 9

Data collected on the same observation unit at a number of points in time are called:

		panel data.
		time series data.
		cross-section data.
		none of the above.

Question 10

A measure of how much the coefficient would vary in regressions based on different samples is called:

		F-statistic.
		standard error of the estimated coefficient.
		t-statistic.
		partial F-statistic.

Question 11

The test statistic used to test the hypothesis of whether a regression coefficient is significantly different from zero, holding all other independent variables constant, is called a(n):

		t-test.
		F-test.
		multicollinearity test.
		autocorrelation test.

Question 12

Regression analysis that analyzes the relationship between one dependent variable and several independent variables is called:

		cluster analysis.
		correlation analysis.
		multiple regression analysis.
		simple regression analysis.

Question 13

The ratio of the regression coefficient to its standard error is called:

		F-statistic.
		t-statistic.
		coefficient of determination.
		partial F-statistic.

Question 14

The coefficient of determination will range between what values?

		-1 and +1
		0 and 1
		-3 and +3
		none of the above

Question 15

The range of values in which we can be confident that the true regression coefficient lies within a given degree of probability is called a:

		confidence interval.
		logistic regression.
		prediction interval.
		none of the above.

Question 16

The estimated regression equation is Y = 10 + 2.5X, if X =0 than the predicted value of Y is equal to

		2.5
		7.5
		12.5
		10

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ADMS 2320 Lecture Notes - Lecture 5: Normal Distribution, Probability Distribution, Standard Deviation

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