Q1 (a) As part of an investigation into levels of overtime working, a company decides to tabulate the number of orders received weekly and compare this with the total weekly overtime worked to give the following Week
1
2
3
4
5
6
7
8
9
10

Orders received
83
22
107
55
48
92
135
32
67
122

Total overtime
38
9
42
18
11
30
48
10
29
51

Using the method of least squares obtain the regression equation of total overtime on orders received and predict the level of total overtime necessary for 100 orders (7 marks)
(b) As a result of tests of 20,000 electric bulbs manufactured by a company it was found that lifetime of the bulbs are normally distributed with an average life of 2040 hours and standard deviation of60 hours. On the basis of the information, estimate the number of bulbs expected to burn for;
(i) More than 2150 hours
(ii) Less than 1960 hours​

What is the absolute value of the complex number -4-sqrt2i

60 musicians applied for a job at a music school. 14 of the musicians play both guitar and drums. what is the probability that the applicant who gets the job plays drums or guitar?

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above