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Answer:
We assume the condition of independence satisifed.
We need to check the following conditions in order to use the normal approximation.
So we see that we satisfy the first condition, but the second no so then we can't apply the approximation for this case, since we need both conditions at the same time in order to use the normal approximation.
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 to the problem
We assume the condition of independence satisifed.
We need to check the following conditions in order to use the normal approximation.
So we see that we satisfy the first condition, but the second no so then we can't apply the approximation for this case, since we need both conditions at the same time in order to use the normal approximation.