Question

One-fifth of the population is left-handed. A random sample of 20 people is selected.

a) What is the probability that no more than 6 of the next 20 people are left-handed.

b) What is the probability that at least 4 of the next 20 people are left-handed.

Answer 1

Try using the binomial probability formula or the binomial probability table.
Using a binomial probability table is much easier.
For a): n = 20; x = 0, 1, 2, 3, 4, 5, 6; p = .20
When you find the probabilities for each x, add all of them together for your total probability.
For b): n = 20; x = 4 through 20; p = .20
When you find all the probabilities for each x, add all of them together for your total probability.
OR... and this is easier... you can find x = 0, 1, 2, 3. (You will already have these probabilities from part a.) Add together, then subtract from 1 for your total probability.

I hope this will help get you started.