IC50005 Mock Test PART B
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AH2022
IC50005 Mock Test
PART B
[120 minutes]
Question 1
Calculate the descriptive statistics for each machine (mean, median, and standard deviation) and comment on statistical values by comparing both machines.
|
Observation |
Weight Machine 1 |
Weight Machine 2 |
|
1 |
20.5 |
10.5 |
|
2 |
51.6 |
50.6 |
|
3 |
14.5 |
45.6 |
|
4 |
44.6 |
63 |
|
5 |
60.3 |
32.4 |
|
6 |
30.5 |
35.4 |
|
7 |
68.6 |
43.2 |
|
8 |
70.5 |
32.8 |
|
9 |
90.5 |
51.2 |
Solution:
|
Observation |
Weight Machine 1 (x) |
x − |
(x − |
|
1 |
20.5 |
-29.68 |
880.77 |
|
2 |
51.6 |
1.42 |
2.02 |
|
3 |
14.5 |
-35.68 |
1272.90 |
|
4 |
44.6 |
-5.58 |
31.11 |
|
5 |
60.3 |
10.12 |
102.46 |
|
6 |
30.5 |
-19.68 |
387.21 |
|
7 |
68.6 |
18.42 |
339.38 |
|
8 |
70.5 |
20.32 |
412.99 |
|
9 |
90.5 |
40.32 |
1625.88 |
|
n = 9 |
∑x = 451. 6 |
|
∑ (x − |
x = 
= 50.18 [1 mark]
Q2 = = = = 5th value (position), hence Q2 = 60.3 [1 mark]
2 2 2
s = 
= 25.14 [1 mark]
|
Observation |
Weight Machine 1 (x) |
x − |
(x − |
|
1 |
10.5 |
-30.02 |
901.33 |
|
2 |
50.6 |
10.08 |
101.56 |
|
3 |
45.6 |
5.08 |
25.78 |
|
4 |
63 |
22.48 |
505.25 |
|
5 |
32.4 |
-8.12 |
65.97 |
|
6 |
35.4 |
-5.12 |
26.24 |
|
7 |
43.2 |
2.68 |
7.17 |
|
8 |
32.8 |
-7.72 |
59.63 |
|
9 |
51.2 |
10.68 |
114.01 |
|
n = 9 |
∑x = 364. 7 |
|
∑ (x − |
x = 
= 40.52 [1 mark]
Q2 = = = = 5th value (position), hence Q2 = 32.4 [1 mark]
2 2 2
n−1
Intepreation: [1 mark]
[1] mark for each mean, median and standard deviation and 1 mark for the interpretations. Full working must be shown, including formulae.
Question 2 [3]
Elena has 6 pairs of black shoes, 5 pairs of white shoes, and 4 pairs of green shoes. She picks two pairs of shoes at random, without replacement. Calculate the probability that she chooses two shoes of the same colour.
Solution:
Black = 6 White = 5 Blue = 4
The total number ofpair of shoes = 6+5+4= 15
P (Black, Black ) = P (Black ) and P (Black ) = 
=
[0.5 mark]
[0.5 mark]
P (White, White) = P (White) and P (White) = 
=
4 3 12
15 14 210
[0.5 mark]
[0.5 mark]
Therefore the probability of choosing two pair of shoes of the same colour :
P (Two pair of same − colour shoes ) =
P (Black, Black ) or P (White, White) or P (Green, Green )
30 20 12 62 31
= + + = =
210 210 210 210 105
[1 mark]
[0.5] mark for total, [0.5] mark for the probability of each colour of two socks, and 1 mark for the final correct answer.
Question 3 [5]
Draw a Box and Whisker plot for the dataset:
[11, 4, 20, 28, 9, 30, 15, 38, 17, 43, 23]
Make sure you label the axis and show the complete workings of your quartile calculations.
Solutions:
Step 1: Arrange the data in ascending order.
Step 2: Find the median. Q2 = 
=20 [1 mark]
Step 3: Split the datasets into two equal sets and find the lower quartile and upper quartile.
|
4 |
9 |
11 |
15 |
17 |
20 |
23 |
28 |
30 |
38 |
43 |
|
Min |
|
|
|
|
|
|
|
|
|
Max |
[2marks]
Step 4: Draw the boxplot and whiskers
[2 marks]
[1] mark for median and [1] mark for lower quartile, [1] mark for upper quartile and [2] marks for the boxplot. Full working must be shown, including formulae.
Question 4 [5]
If S is a sample space, and E and F are the events with: P(E) =0.4, P(F) = 0.6, and P(E and F) = 0.2. (a) What is P(E|F)? [2.5 points]
(b) What is P (F|E)? [2.5 points]
Solution:
(a) P(E F)
= = = = 33.33% [2.5 mark]
(b) P(E F)
= = = = 50% [2.5 mark]
P(E) 0.4 2
[1] mark for formula, [0.5] for ratio and [1] for the final answer. Full working must be shown, including formulae.
2022-08-30