Answer:
0.15651
Step-by-step explanation:
This can be approximated using a Poisson distribution formula.
The Poisson distribution formula is given by
P(X = x) = (e^-λ)(λˣ)/x!
P(X ≤ x) = Σ (e^-λ)(λˣ)/x! (Summation From 0 to x)
where λ = mean of distribution = 20 red bags of skittles (20% of 100 bags of skittles means 20 red bags of skittles)
x = variable whose probability is required = less than 16 red bags of skittles
P(X < x) = Σ (e^-λ)(λˣ)/x! (Summation From 0 to (x-1))
P(X < 16) = Σ (e^-λ)(λˣ)/x! (Summation From x=0 to x=15)
P(X < 16) = P(X=0) + P(X=1) + P(X=2) +......+ P(X=15)
Solving this,
P(X < 16) = 0.15651
