According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags of Skittles, what is the probability that the proportion in our sample of red candies will be less than 16%?

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