QEAD Rev:03ver 01 9th July 2017Template A3
F/QAP/021/001
| Q1 Q2 Q3 Q4 |
Use Stokes theorem to compute the flux of the curl of a vector field ⃗ ( ) ⃗ out of the rectangular parallelepiped surfaces above the XOY-plane In a continuous distribution, the probability density function is given by ( ) {√ I. Find the value of II. Compute the probability ( ) III. Determine the cumulative distribution function CDF For the Given vector field ⃗ i. Compute the divergence of the vector field . ii. Find the vector value of ( ) The following data give the resting pulse rate (in beats per minute) and the years of schooling of 10 individuals. Find the Karl Pearson’s coefficient of correlation. Also comment on the value obtained. Years of school 12 16 13 18 19 12 18 19 12 14Pulse rate 73 67 74 63 73 84 60 62 76 71 |
[10] [3] [3] [5] [5] [5] [5] |
QEAD Rev:03ver 01 9th July 2017Template A4
F/QAP/021/001
| Q5 Q6 Q7 Q8 |
How much work is required to move an object in the vector field ⃗ Along the curve , consisting of three line segments as shown in the figure: At the conclusion of Eligibility examination for admission into engineering courses at military technological college, data was collected by the Bureau of statistics for the purpose of conducting different surveys. It has been found that the mean height of 800 examinees is 175 cm and standard deviation is 5cm. If we assume the heights are Normally Distributed, determine the number of examinees likely to have heights: i. More than 180cm ii. Less than 170cm iii. Between 178cm and 188 Verify Green’s theorem for ∮ ( ) ( ) Where C is the boundary of the triangle formed by and . New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval? |
[10] [15] [10] [10] |
QEAD Rev:03ver 01 9th July 2017Template A5
F/QAP/021/001
| Q9 Q10 Q11 Q11 |
For the vector filed ⃗ i. Show that ⃗ is Irrotational field. ii. Compute the scalar potential function of this conservative field If the underlying incidence rate of chronic bronchitis in the first year of life is 0.05. Use the binomial distribution to compute the probability of obtaining at least 5 cases of chronic bronchitis in the first year of life among 8 families in which both parents have chronic bronchitis. In a communication network, packets of information travel along lines. The number of lines used by each packet varies according to the following table: Number of lines used 1 2 3 4 5Number of packets 17 54 32 6 1Calculate the Total mean number of lines used per packets. Use the Vector integral theorem to the find the flux of the vector field ⃗ ( ) ( ) ( )⃗ out of , where S is the surface of the solid cone bounded by the surface √ and the plane . |
[6] [5] [5] [6] [10] |
| Q12 |
QEAD Rev:03ver 01 9th July 2017Template A6
F/QAP/021/001
| Q12 Q13 Q14 |
A random sample of 40 engineers shows a mean of $145580 and standard deviation $13200 as yearly income. Construct 95% confidence interval for the population mean A manufacturer supplies nominal capacitance of 25 Mw (megawatts) and standard deviation of 0.98 mw capacitors. A random sample of 80 such capacitors was taken, and found to have a mean capacitance 24.79 mw. Use the P value to test at 5% level of significance whether there is evidence that the mean capacitance of the entire supply is more than 25 Mw. A popular automotive company has launched a new version of a sports car on the market, which supposedly has less gasoline consumption than the predecessor model. The producer states that the new model has an average consumption of 8 liter per 100 Km. the standard deviation of the consumption is assumed to be liter and the average consumption in 50 test drives has been 8.5 liter per 100 km. i. Decide whether the information provided by the producer is credible. Use the hypotheses test with significance level of 10% ii. Would the test decision be the same if the standard deviation of the consumption were liter? |
[7] [10] [5] [5] |
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