IB Maths AA SL 4.8 Binomial distribution Question Bank

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

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.

Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.

recognizing binomial probability
eg $\quad X \sim \mathrm{~B}(n, p),\binom{n}{r} p^{r} q^{n-r},(0.016327)^{2}(0.983672)^{8},\binom{10}{2}$
valid approach
eg $\mathrm{P}(X \geq 2)=1-\mathrm{P}(X \leq 1), 1-\mathrm{P}(X<a)$ , summing terms from 2 to 10 (accept binomcdf( 10,0.0163,2,10 ) )
0.010994
$\mathrm{P}(X \geq 2)=0.0110$

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SL 4.8—Binomial distribution question 1