Answer:
Using the binomial distribution we can find this probability with the following excel code:
"=BINOM.DIST(30,200,0.1,TRUE)", and we got:
Using the normal approximation
We can use the continuity factor correction:
And we can use the z score formula given by:
And we got:
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:
We want to find this probability;
Using the binomial distribution we can find this probability with the following excel code:
"=BINOM.DIST(30,200,0.1,TRUE)", and we got:
The other way is using the normal approximation for the binomial distribution
We need to check the conditions in order to use the normal approximation.
So we see that we satisfy the conditions and then we can apply the approximation.
If we appply the approximation the new mean and standard deviation are:
And we can use the continuity factor correction:
And we can use the z score formula given by:
And we got: