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1 of 8 0-day streak

Binomial conditions, the distribution table and graph shape

Question 1 of 8

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Consider the following repeated-trial situation

A procedure continues until a stopping rule is met, so the number of trials is not fixed

Decide whether this situation can be modelled by a binomial distribution

For the distribution table below, use a separate binomial variable with \(n=3\) and \(p=2/3\)

Binomial probability distribution
\(x\)\(\Pr(X=x)\)
\(0\)\(\square\)
\(1\)\(\square\)
\(2\)\(\square\)
\(3\)\(\frac{8}{27}\)
(a)1 mark

Does the described situation meet the conditions for a binomial distribution?

(b)3 marks

Calculate the missing entries in the probability distribution table

(c)1 mark

Find \(\Pr(X=1)\) from the table

Format: exact fraction