Let X be the number of a graduate assistants.
⇒ X = 8
Let p be the probability of the assistant studying at the office.
Then, q be the probability of the assistant studying at home.
According to the question, each assistant is just likely to study at home as in the office.
Also, we know that (p + q) = 1.
⇒ q = 1 – p
Now, let there be k number of desks in the office.
We need to find the number of desks in the office so that each assistant has a desk at least 90% of the time.
⇒ P (X > k) < 0.10
Now, we must find a value of k that satisfies the above equation.
P (X > 5) = P (X = 6 or X = 7 or X = 8)
⇒ P (X > 5) = 0.14
Also, P (X > 6) = P (X = 7 or X = 8)
⇒ P (X > 6) = 0.035
∴, P (X > 6) < 0.10
Hence, if there are 6 desks, then there is atleast 90% chance for every graduate assistant to get a desk.
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