Answer:
a)
We expect 2.4 successes in a sample of three selected.
And the standard deviation is given by:
Represent the typical variation around the mean.
b)
And we want this probability:
c)
And we want this probability:
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".
Solution to the problem
Part a
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:
And we want the following probabilities
The mean is given by:
We expect 2.4 successes in a sample of three selected.
And the standard deviation is given by:
Represent the typical variation around the mean.
Part b
Let Y the random variable of interest, on this case we now that:
And we want this probability:
Part c
Let Z the random variable of interest, on this case we now that:
And we want this probability:
