IB Maths AA SL 4.8 Binomial Distribution Questions

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

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.

[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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IB Maths AA SL 4.8 Binomial Distribution Questions question 1