STAT319_Finalexam_A.pdf
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(2) PART I: (10 Marks) Q1] A coin has (Head, Tail) is tossed two times. (6 Marks) Q1.a] Find the probability distribution of the random variable “Number of Tail”? (1 Marks, 0.25 Mark for each cell) Number of Tail x. Probability p(x). 0 1 2 TOTAL. Q1.b] Use the table in Part Q1.a, to calculate E(X) and V(X)? . Solution: (3 Marks, 0.25 Mark for each cell). X 0 1 2. p(x). X . p(x). X2 . p(x). Total Solution: (2 Mark for each) E(X) = V(X) = Q2]. The following data consists of the weights by pounds of 20 person adults: 55, 62, 77, 89, 75, 88, 64, 50, 61, 59, 71, 82, 74, 51,63,84,78, 66, 54, 57 Using the following table to calculate:. (4 Marks, 0.25 Mark for each cell).. 1. Relative Frequency. 2. Cumulative Frequency Distributions. 3. And Cumulative Relative Frequency. Class Intervals. Frequency. Relative Frequency. Cumulative Frequency. Cumulative Relative Frequency. 50 - 60 61 - 70 71 - 80 81 - 90. Page (2) / 8.
(3) PART II: (7 Marks) Q3]. In a small town with two schools, 1000 students were asked if they had a cell phone. The results of the survey are shown below: (3 Marks, 1 Mark for each).. School A School B Total . Students who have a cell phone. Students who do not have a cell phone. Total. 365 408 773. 156 71 227. 521 479 1000. Find the following random selected probabilities :. Q3.a) Find the probability of a randomly selected student from School B? Solution:. Q3.b) Find the probability of a randomly selected student has a cell phone given that the student attends School B? Solution:. Q3.c) Find the probability of a randomly selected student has a cell phone and these from School B? Solution:. Q4]. Write any 2 properties of the following: (4 Marks) Q4.a) Probability Mass Function (2Marks). Q4.b)Probability Density Function (2Marks). Page (3) / 8.
(4) PART III: (8 Marks, 1 Mark for each) Q5]. Determine the correct answer, and then fill the table below: 1) If the sample size equal 15 and the 2) One of the following point is not from residuals equal 40 what is the estimated. engineering Application of Statistics:. for the Residuals and the Standard Error: a)11.547. a) Model Building and Predicting.. b)11.088. b) Mathematical Algebra.. c)11.447. c) Assessing Design Reliability.. 3) Calculate. the. Standard. deviation. 4) Statistical __________ define is helpful. Coefficient if the Variation equals 11 and. in making choices regarding designs,. the mean equal 30?. materials, procedures, technologies or methods.. a)330.32. a) Analyses.. b) 330.43. b) Methods.. c) 330.00. c) Descriptive.. 5) In the Statistical population we use two. 6) Fill the blanks, if the correlation. plot diagrams, the first called Scatter. greater than 0.8 is generally described. Diagram. for. __________Population. as ________, but if a correlation less. Variables,. and. the. than 0.5 is generally described as. second. called. Crosstabulation for__________Population. _________.. Variables. a) Interval, Ordinal.. a) Weak, Strong.. b) Quantitative, Qualitative. b) Strong , Strong.. c) Ratio, Nominal.. c) Strong , Weak.. 7) What is the Skewness Coefficient if the Standard deviation equals 10and the mean. 8) One of the following point is not from Frequency distributions :. 30 and the median equal 15? a) 4.5. a) Uniform Distribution.. b) 4.6. b) Exponential Distribution.. c) 4.1. c) Nonlinear Regression Distribution.. Solution 1. 2. 3. 4. 5. 6. 7. 8. Page (4) / 8.
(5) PART IV: (7 Marks) Q6.a] Compare Qualitative data and Quantitative data: (2 Marks, 0.5 Mark for each cell). Quantitative Data. Qualitative Data. Q5.b]. Indicate whether Deductive or Inductive statistics best categories the following cases:. (2 Marks, 1 Mark for each cell). Status. Categories. 1. A professor knows test score of 85 students in her class. If she selects 25 students at random, she can know the average scores. 2. Twelve randomly chosen electrical engineering majors are tested to determine how well complex variables are understood by university students. Q5.c]. Find interquartile Range then draw the Box Plots 115.4 115.4. 115.7. 116.0. 116.1. When: Q.25=115.45 and Q.75=116.45. 116.2. 116.4 116.5 116.6 (3 Marks). Solution:. Page (5) / 8.
(6) PART V: (13 Marks) Q7.b] Survey determines that in a particular town, 33% of the residents jog, 42% bike and 12% do both activities. Use general addition law to calculate that probability what a randomly selected person does neither activity?. (2 Marks). Solution:. Q7.a] Transform the curvilinear regression line using And. X =2 The curvilinear regression line is:. (4 Marks). Yˆ = ln Y Yˆ = a.b ( 500 / X ). Solution:. Page (6) / 8.
(7) Q7.c] Consider the data relating the area of aquifer contamination Y(acres)to the time X(years) after release of toxic chemical. Use curvilinear regression in fitting a curve of form:. (7 Marks, 0.25 Mark for each cell). X. 1.3. 2.4. 3.6. 4.4. Y. 0.5. 6.2. 1.5. 4.8. ln Y. X.ln Y. Solution: X. Y. X2. Total (1 Mark for each). ln b=. ln a=. Page (7) / 8.
(8) Best Wishes.... Instructor signature ______________________. Internal examiner signature ________________.. Page (8) / 8.
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