IOP2601 ASSIGNMENT 2 SEMESTER 2 2024 Given a normally distributed population with a mean (μ) of 10, a standard deviation (σ) of 2, and 50 as the number of students (N), answer the following questions: A Nigerian researcher conducted a study on the im

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Question 1 (11 marks)

Use the information below to answer the questions that follow.

A local community centre will soon be celebrating its annual "Volunteer of the Year"
award, with the winner receiving a R20 000 gift card and a certificate of appreciation.
Two volunteers, Sonia and Jack, are finalists for this prize. Sonia has been
volunteering at the centre for fifteen (15) years and is recognised for her dedication
and vast contributions. She received 40 nominations from various community
members. Jack is a new volunteer who has made a big impact with his energy and
innovative ideas. He received 20 nominations from both community members and
employees. The community centre's administration received 200 valid nominations.
Sonia and Jack are now excitedly anticipating the announcement of the winner,
conscious that their chances are determined by the number of nominations they
received, as well as the selection committee's considerations.

1.1 What is the probability that Sonia will win first prize?
Total nominations = 200
Sonia's nominations = 40
𝑆𝑜𝑛𝑖𝑎′ 𝑠 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠
Probability = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠
40
P(Sonia wins) = 200 = 0.20


1.2 What is the possibility that Jack will win first prize?
Jack's nominations = 20
𝐽𝑎𝑐𝑘 ′ 𝑠 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠
Probability = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠

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