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IB Maths AA HL Sl 4 8 Binomial Distribution Questions

Practise deciding when a binomial model is appropriate, then calculating its mean, variance and probabilities with suitable technology.

Syllabus
First assessment 2021
Course
Mathematics: analysis and approaches HL
Level
HL

Exam points

  • Recognise when a binomial distribution is an appropriate model by checking fixed trials, two outcomes, constant success probability and independence.
  • Use technology or the binomial model to calculate probabilities, mean np and variance np(1−p), interpreting the result in context.

IB Maths AA HL Sl 4 8 Binomial Distribution Questions question 1

[Maximum number: 5]

Amanda enters data from surveys into a database. It can be assumed that the accuracy of any survey entered is independent of all other surveys entered.
From previous records, it is known that Amanda enters 8 % of the surveys inaccurately.

Question (a)

(a)

On a particular day Amanda enters data from 50 surveys.

[ 2 ]

Question (i)

(i)

Find the probability that Amanda entered at most six surveys inaccurately.

[ 2 ]

Question (b)

(b)

Find the value of n.

Bryce and Carmen also enter data from surveys into the same database. It is known that surveys entered by Bryce and Carmen are inaccurate 6 % and 11 % of the time respectively. It can again be assumed that the accuracy of any survey entered is independent of all other surveys entered.

From the surveys assigned to the three of them, Amanda enters 55 %, Bryce 25 % and Carmen 20\%.

[ 3 ]
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