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2 answers:
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Answer:
a)
And replacing we got:
b) D. No, because the probability of this occurring is not small.
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".
Part a
If 15 people are randomly selected, find the probability that at least 13 of them have brown eyes.
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 to find this probability:
And replacing we got:
Part b
Is it unusual to randomly select 15 people and find that at least 13 of them have brown eyes? Note that a small probability is one that is less than 0.05.
Since our calculated probability is too higher compared to 0.05 we can conclude this:
D. No, because the probability of this occurring is not small.