Answer :

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.

Clearly,

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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