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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 check is applied to a fixed number of units. Each unit gives success or failure independently, with one constant success probability

Decide whether this situation can be modelled by a binomial distribution

For the distribution table below, use a separate binomial variable with \(n=4\) and \(p=7/10\)

Binomial probability distribution
\(x\)\(\Pr(X=x)\)
\(0\)\(\square\)
\(1\)\(\frac{189}{2500}\)
\(2\)\(\square\)
\(3\)\(\frac{1029}{2500}\)
\(4\)\(\square\)
(a)1 mark

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

(b)3 marks

Fill in the missing probabilities in the table

(c)1 mark

Calculate \(\Pr(X=0)\) using the distribution

Format: exact fraction