Answer:
a)
And then we have our probability distribution like this:
X | 0 | 1 | 2 |
P(X) | 0.7921 | 0.1958 | 0.0121|
b)
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution for the problem
Part a
On this case since we select a sample size of n =2 we have the following values for the number of left handed X=0,1,2. We can find the probabilities for each case since we know that p=0.11.
And then we have our probability distribution like this:
X | 0 | 1 | 2 |
P(X) | 0.7921 | 0.1958 | 0.0121|
Part b
For this case we want this probability: