Hi,
Here are the answers, for reference:
Q1 {k is real : 0 < k < 8}
Q2(ii) x = -1.1116, 1.5995
(iii) 3.615 sq units
Q3(i) (1/3)e^(3x + 2) + c
(ii) 32
Q4 16/27 cu m
Q5(i) (1/2, (1/2) - ln 2)
(ii) A ((16/5) - (3/5)ln 5, 0), B (0, (16/3) - ln 5), p = 16, q
= 3
Q6 0.1, 0.4
Q7(i) Every student has the same probability (of 1/2000) of
being chosen to be in the sample.
(ii) Stratum 1: Travel by car, sample size = 22
Stratum 2: Travel by bicycle, sample size = 38
Stratum 3: Travel on foot, sample size = 40
(iii) Stratified sampling gives a sample that is representative
of the population of students travelling by various means. Have two
futher strata Year 1 and Year 2 so that the sample will also
reflect the composition by years.
Q8(ii) r = -0.967
(iii) T = -0.0147H + 27.0
(iv) 12.3, Reliable since 1000 is within the range [200,
1550].
Q9 p-value = 0.00578
There is sufficient evidence, at 1% significance level, that
this particular batch is substandard.
Least T = 11700
Q10(i)(a) 0.0287
(b) 0.852
(ii) 0.201
(iii) 0.974
Q11(i)(b) 11/16
(c) 2/11
(ii) 163/315
Q12(i) 0.595
(ii) 0.739
(iii) 0.787
(iv) 408
Thanks.
Cheers,
Wen Shih