IB Maths AA HL 4.8 Binomial distribution Question Bank

Practise IB Mathematics SL/HL 4.8 by applying binomial distribution methods to exam-style questions.

[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.

(a)

On a particular day Amanda enters data from 50 surveys.

[ 2 ]

(i)

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

[ 2 ]

recognizing binomial distribution
$E \sim \mathrm{~B}(50,0.08)$ , where E is the number of inaccurate surveys
$\mathrm{P}(E \leq 6)=0.898128 \ldots$ $(\mathrm{P}(E \leq 6)=) 0.898$ (accept 89.8 % )

(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 ]

use of tables

Note: Award (M1) for at least one correct value of $\mathrm{P}(E \leq 6)$ for a value of n, where $n \neq 50$ .

(n=94 \Rightarrow) \mathrm{P}(E \leq 6)=0.366746 \ldots

n=94

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SL 4.8—Binomial distribution question 1

Question (a)

Question (i)

Question (b)