Answer:
a) Figure attached
b)
c) For the case n= 6
For the case n= 5
So then we need at least n=5 or n=6 to satisfy the condition required.
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
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:
Part a
For this case we can use the following R code:
> x <- seq(0,9,by = 1)
> y <- dbinom(x,9,0.7)
> plot(x,y,main="Histogram",type = "h")
And we can see on the figure attached the solution.
We see that the higher probabilities are from 4 to 9
Part b
The expected value is given by:
The variance is given by:
And the standard deviation is:
Part c
First we can find the probability that at least two addresses will be found in the list of 9 that we have like this:
We can use the complement rule and we have:
We find the indicidual probabilities:
If we use the case of n=8 and we find , we got:
For the case n= 7
For the case n= 6
For the case n= 5
So then we need at least n=5 or n=6 to satisfy the condition required.
