2023HSCShort answer

Q12 (c) (i)

2 marks

Question

A gym has 9 pieces of equipment: 5 treadmills and 4 rowing machines.

On average, each treadmill is used 65% of the time and each rowing machine is used 40% of the time.

(i) Find an expression for the probability that, at a particular time, exactly 3 of the 5 treadmills are in use.

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct answer	2
Demonstrates some understanding of binomial probability, or equivalent merit	1

Sample answer:

{}^5C_3(0.65)^3(0.35)^2

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Syllabus alignment

Statistical Analysis

The Binomial DistributionModel Bernoulli trials with binomial random variables and use binomial probabilities and summary measures to analyse chance processes.

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