统计代考代做 Statistics代写统计代写

Statistics I Exam

Duration: 2h+30m

统计代考代做 QUESTION 1 [4,5/20] An international organization intends to study the relation between per capita income (103 €) and the weight (%) of R&D

QUESTION 1 [4,5/20]

An international organization intends to study the relation between per capita income (103 €) and the weight (%) of R&D (Research & Development) expenses in the GNP (Gross National Product) of each country. The following table shows the results for 2005 for a sample of 100 countries:

(1,5) a) Construct a frequency polygon for the distribution of % R&D in GNP.

(3,0) b) Comment about the truth of the following sentences:

b₁) “The average weight of R&D in GNP, for this sample of 100 countries, is 1.975%”.

b₂) “In most of these countries, the percentage of R&D in GNP is 1%”.

b₃) “Per capita income is higher than 40.000€, only for 10% of the countries”.

b₄) “Half of the countries have per capita income between 10.000€ and 32.500€ “.

QUESTION 2 [3/20] 统计代考代做

A company produces only three different types of brooms (A, B and C), with 40% and 20% of the production being types B and C, respectively. According to information given by the quality control department, 5% of the total production is defective because it has a width lower than the accepted value, and 17.5% of type C brooms present the same problem. They also know that 30% of the defective brooms are type B.

a) Calculate the probability of a type B broom being defective, i.e., having a width lower than the accepted value.

b) What is the percentage of type A in the total number of defective brooms?

QUESTION 3 [3/20] 统计代考代做

Given the random variable X , it is known that E[X ] = 6 and that E[X² ] = 62. Consider another random variableY , such that Y = ⅓ X + 1 .

(1,5) a) Calculate E[Y] and Var[Y ] .

(1,5) b) What can you say about the linear correlation between X and Y? Justify your answer without any further calculations.

QUESTION 4 [3/20] 统计代考代做

A group of researchers wants to carry out a study about stress. They know that 45% of the population suffers from stress.

(1,5) a) In a group of 15 people, what is the probability that at least one suffers from stress?

(1,5) b) They want their study to be based on a sample group of n people. But, for the study to be successful they need to find in this group one person that suffers from stress, with probability of at least 0.90. What should be the minimum dimension for the sample group?

QUESTION 5 [4/20] 统计代考代做

A company operates in two different zones: North and South Lisbon. Sales for each day (in monetary units) show a normal distribution with parameters (100;10) and (150;30), respectively for North and South Lisbon.

(1,0) a) Calculate the probability that total sales, in one day, are higher than 270 monetary units.

(1,5) b) Suppose now that the company manager wants to set a prize for quarter sales (60 days). What should the value of the prize so that the probability of being awarded is 0.4?

(1,5) c) The company is carrying on a daily control of sales for the current month (20 working days). What is the probability that, in 20% of the days, the total value of the sales is less than 200 monetary units?

QUESTION 6

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