57.
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Answer:
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
54% of the school's graduates move to a different state after graduating.
This means that
7 randomly selected graduates
This means that
Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Either none moves, or at least one does. The sum of the probabilities of these events is 1. So
We want . Then
In which
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.