IOP2601
ASSIGNMENT 2 SEMESTER 2 2024
, QUESTION 1
80
1.1. 𝑃(𝑌𝑎𝑛𝑔𝑎 𝑤𝑖𝑙𝑙 𝑤𝑖𝑛 𝑓𝑖𝑟𝑠𝑡 𝑝𝑟𝑖𝑧𝑒 ) = = 0.20
400
60
1.2. 𝑃(𝐼𝑛𝑔𝑎 𝑤𝑖𝑙𝑙 𝑤𝑖𝑛 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑟𝑖𝑧𝑒 ) = = 0.1504
399
80 60
1.3. 𝑃(𝑌𝑎𝑛𝑔𝑎 𝑎𝑛𝑑 𝐼𝑛𝑔𝑎 𝑤𝑖𝑙𝑙 𝑤𝑖𝑛 𝑓𝑖𝑟𝑠𝑡 𝑎𝑛𝑑 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑟𝑖𝑧𝑒𝑠 ) = 2 ( 400 ∗ 399) = 0.0602
QUESTION 2
2.1. Proportion of students with a raw score of greater than 9
𝑋− 𝜇
𝑧=
𝜎
4 − 12
𝑧= = −4
2
𝑃(𝑧 > −4 ) = 1
2.2. Percentage of students with a raw score less than 16
𝑋− 𝜇
𝑧=
𝜎
16 − 12
𝑧= =2
2
𝑃(𝑧 < 2 ) = 0.9772 × 100 = 97.72%
ASSIGNMENT 2 SEMESTER 2 2024
, QUESTION 1
80
1.1. 𝑃(𝑌𝑎𝑛𝑔𝑎 𝑤𝑖𝑙𝑙 𝑤𝑖𝑛 𝑓𝑖𝑟𝑠𝑡 𝑝𝑟𝑖𝑧𝑒 ) = = 0.20
400
60
1.2. 𝑃(𝐼𝑛𝑔𝑎 𝑤𝑖𝑙𝑙 𝑤𝑖𝑛 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑟𝑖𝑧𝑒 ) = = 0.1504
399
80 60
1.3. 𝑃(𝑌𝑎𝑛𝑔𝑎 𝑎𝑛𝑑 𝐼𝑛𝑔𝑎 𝑤𝑖𝑙𝑙 𝑤𝑖𝑛 𝑓𝑖𝑟𝑠𝑡 𝑎𝑛𝑑 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑟𝑖𝑧𝑒𝑠 ) = 2 ( 400 ∗ 399) = 0.0602
QUESTION 2
2.1. Proportion of students with a raw score of greater than 9
𝑋− 𝜇
𝑧=
𝜎
4 − 12
𝑧= = −4
2
𝑃(𝑧 > −4 ) = 1
2.2. Percentage of students with a raw score less than 16
𝑋− 𝜇
𝑧=
𝜎
16 − 12
𝑧= =2
2
𝑃(𝑧 < 2 ) = 0.9772 × 100 = 97.72%
