Econs Case Study

MS 3229

2012/2013 SEMESTER ONE – CLASS TEST DEWT/ DCEB 2FT - ENGINEERING MATHEMATICS 2 Time Allowed: 30 mins Instructions To Candidates: 1. 2. 2. 3. 4. 1. All the SP exam rules are to be complied with.

A ‘mathematical formulae and tables’ card is provided.
All non-exact answers are to be corrected to 3 significant figures All answers are to be written in the answer booklet provided. Answer ALL the THREE questions. The level of pollution (measurements y in coded units) in a city and the corresponding temperature and humidity index (measurements x ) were recorded at noon on 10 different days. Elementary calculations yielded

x i i

 652

y i i

 192

x y i i

i

 14027

x i 2

i

 46122

y i 2

i

 4608

A scatter plot indicates a linear trend. (a) (b) (c) Find the correlation coefficient, r , and comment on its value. Show that this trend is positive. Estimate the level of pollution at noon on a day when the temperature and humidity index is 75. (Note that over the 10 days, the temperature and humidity index ranged from 30 to 95)
(15 marks)

2.

A random variable X

N ( ,  2 )

(a) If   30 ,  2  16 , find the probability of P(X < 33) . (b) If   25 ,  2  9 , find the value of k for P(X > k) = 0.0537
(15 marks)

3.

The length of rods in a large batch with mean 120 mm and a standard deviation of 1.5 mm. (a) (b) What percentage of the rods will have length of more than 122.5 mm? If 10% of rods were to be rejected for being too short, what is the minimum length of the rods that will accept? What is the assumption you have made in your calculation?
(20 marks) END

(c)

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