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.
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.
To answer both questions, we can use the binomial probability formula. The formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes.
- n is the number of trials.
- k is the number of successes.
- p is the probability of success on a given trial.
- (n choose k) is the binomial coefficient, which represents the number of ways to choose k objects from a set of n objects.
Now, let's calculate the probabilities for each question.
a) What is the probability that no more than 6 of the next 20 people are left-handed?
In this case, we need to calculate the probability of getting 0, 1, 2, 3, 4, 5, or 6 left-handed people out of the 20 selected.
P(X <= 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
We can calculate each probability using the binomial probability formula mentioned earlier.
b) What is the probability that at least 4 of the next 20 people are left-handed?
In this case, we need to calculate the probability of getting 4, 5, 6, ..., 20 left-handed people out of the 20 selected.
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = 20)
Again, we can calculate each probability using the binomial probability formula.
By substituting the values into the formula, we can solve for each probability.