Answer:
a) 0.48
b) 0.6645
c) 12.5
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they are left-handed, or they are not. The probabilities of each person being left-handed are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
The number of trials expected to find r sucesses is given by
In this problem we have that:
Assume that 8% of people are left-handed. We select 6 people at random.
This means that
a) How many lefties do you expect?
b) With what standard deviation?
c) If we keep picking people until we find a lefty, how long do you expect it will take?
Number of trials to find 1 success. So