A study conducted at a certain college shows that 61% of the school's graduates move to a different state after graduating. Find the probability that among 9 randomly selected graduates, at least one moves to a different state after graduating. Round to three decimal places as needed.

0.999 is the required probability

Step-by-step explanation:

We are given the following information:

We treat graduates moving to a different state as a success.

P(graduates move to a different state) = 61% = 0.61

Then the number of adults follows a binomial distribution, where

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 9

We have to evaluate:

0.999 is the probability that among 9 randomly selected graduates, at least one moves to a different state after graduating.

Probability that at least one moves to a different state after graduating is 0.999.

Step-by-step explanation:

We are given that a study conducted at a certain college shows that 61% of the school's graduates move to a different state after graduating.

Also, 9 graduates randomly selected and we have to find the probability that at least one moves to a different state after graduating.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 9 graduates

            r = number of success = at least one

           p = probability of success which in our question is % of school's

                graduates moving to a different state after graduating, i.e; 61%

LET X = Number of graduates moving to a different state after graduating

So, it means X ~

Now, Probability that at least one moves to a different state after graduating is given by = P(X 1)

         P(X 1) =  1 - P(X = 0)

                       =  

                       =

                       = = 0.999

Therefore, Probability that among 9 randomly selected graduates, at least one moves to a different state after graduating is 0.999.

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3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

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