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

Recognize when repeated independent trials follow a binomial model and define n and p.
Calculate exact binomial probabilities for a stated number of successes.
Use binomial expectation to estimate a count in a real sampling or business context.

Learn this topic

Study SL 4.8—Binomial distribution conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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
$\mathrm{P}(X \geq 2)=0.0110$

All question bank results loaded

Learn this topic

IB Maths AA SL 4.8 Binomial Distribution Questions question 1