Assignment i Love Statistic

QUESTION 1 Please write an essay entitle ‘I LOVE STATISTIC’ (30 marks) a) Your essay must be: I. Typewritten in English II. Not less than 100 words III. Free from plagiarism. Offenders will get ZERO mark straightaway IV. Relate your essay with civil engineering problem solving and job scope V. Grammatically correct VI. Font to be used – Calibry (body), size 11 b) At the end of your essay, please write your expected mark (example, 89/100) Solution : Statistic is the practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample. Statistics is a discipline which is concerned with designing experiments and other data collection, summarizing information to aid understanding, drawing conclusions from data, and estimating the present or predicting the future. Statistic will cover various applications in civil engineering. Firstly, we can see in field of traffic engineering. In this field, we know the distribution of hourly traffic volume on a proposed highway. We need to find the hourly volume to be used for design to solve The design volume dictates the required number of lanes, etc. For most highways, the design volume is that which corresponds to the 30th busiest hour in the year. Second application, we use statistic in field of surveying and mapping. This is series of measurements from the field, each of which is made using an instrument that has a certain precision. Many measurements in surveying are made using a series of instrument setups. For example, consider a piece of property whose boundary consists of 8 line segments. The orientation of one of these segments with respect to true north is known to a precision of 20" of arc. A surveyor sets up a "total station" (an instrument that measures angles and distances) at each of the 8 corners, and measures the angles to a precision of 20" and the distances to a

precision of 0.01 ft. These measurements are then "adjusted" so that satisfies the rules of geometry. We can observe probability the precision of the computed orientations of the other property lines. For the conclusion, that is some example problem solving in civil engineering and job scope we can related with statistic. This subject BFC34303 is learning the basic statistic we can apply in scope of engineering. I hope this subject I will get at least B in this semester.

Question 2 A supplier converts the weights on the cement packages she sends out from Ounces to kilograms (1kg = 35.27 oz). a. How does this affect the mean weight of the packages? b. How does this affect the standard deviation of the weights? Solution : a) The

mean

weight

of

the

packages

=

mean

weight

of

the

packages/35.27 So, the mean weight of the packages will decrease in 35.27 b) The standard deviation of the weights = the standard deviation/35.27 So, the standard deviation of the packages will decrease in 35.27

Question 3 There are 15 numbers on a list, and the mean is 25. The smallest number on the list is changed from 12.9 to 1.29. a) Is it possible to determine by how much the mean changes? If so, by how much does it change? b) Is it possible to determine the value of the mean after the change? If so, what is the value? c) Is it possible to determine by how much the median changes? If so, by how much does it change? d) Is it possible to determine by how much the standard deviation changes? If so, by how much does it change?

Solution : a) Yes. If the mean is 25 than the sum of all the values is 15 x 25=375. To find the new sum 375 - 12.9 + 1.29 = 363.69 b) Yes. To find the new mean 363.39/15 = 24.226. The change is 0.774. c) The median does not change. d) The standard deviation changes. Standard deviation is : = Sqrt [(sigma X^2/N)-(sigma X/N)^2)] = Sqrt [(363.39^2/15)-(363.39/15)^2)] = Sqrt [(8216.587064)] = 90.645

Question 4

For each of the following say whether it can be the graph of a cdf. If it can be, say whether the variable is discrete or continuous.

Solution : i.

Discrete

ii.

Discrete

iii. Discrete iv. Discrete v.

Continuous

vi. Continuous vii. Continuous viii. Continuous

Question 5 Founder of modern probability and statistics theory Cardano asserted that if one throws a die three times the chance that a given number will show

at least once is 50 percent. This is now recognized as the wrong answer. What is a probability of at least one dice showing 6? Solution : Let A be the required event, and let Ai be defined by: Ai = ”exactly i dice show 6, ” i = 0, 1, 2, 3. Then, P(A) = P(A1 ∪ A2 ∪ A3) = 1 − P(A0) P(A0) = 5/6 × 5/6 × 5/6 = 53/63 = 125/216 = so that P(A) = 1 − 125/216 = 91/216 = 0.4213.