What is the probability no More than 5 of the next 100 will injure themselves?

Answer 1

Since we're setting the number of people to be 100, we'll have a binomial random variable with some probability (you should have a proportion p in your problem that you can sub in). Next, since no more than 5 can be injured, that means we can have 5 or fewer (X≤5). I'll put the general formula below (with summation notation) as well as some ways to find this using some calculators (TI 84, Excel, and R).

Summation notation

∑₀⁵ ₁₀₀C_x•p^x•(1-p)^100-x

TI 84

binomcdf(100, p, 5)

Excel

binom.dist.range(100, p, 0, 5)

R

pbinom(5,100,p)

So whatever your proportion is, simply plug that in and you should have your answer.