Assessing Binomial Model Validity

00:00 5 marks

This question requires you to evaluate the validity of parameters used in a binomial experiment and then correctly apply the binomial probability formula under valid conditions. Consider the conditions under which the binomial model is valid and ensure you check the boundaries for n and p before proceeding to calculation.

Part a

4 minutes 3 marks

Question

Consider a binomial experiment with parameters n = -5 and p = 1.2. Explain why these parameters are invalid for a binomial distribution and list the necessary conditions that n and p must satisfy.

Hint Hint

Hint

Recall that n must be a positive integer and p must lie within the interval [0, 1].

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Complete Answer

The parameters are invalid because n must be a positive integer (n > 0) and p must be between 0 and 1 (0 \(\leq p \leq 1\)).

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Part b

3 minutes 2 marks

Question

For a valid binomial experiment with n = 10 and p = 0.3, use the binomial probability formula to calculate the probability of exactly 3 successes.

Hint Hint

Hint

Recall the binomial formula: \(P(X=k)=\binom{n}{k} p^k (1-p)^{n-k}\).

Answer Answer
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Answer Answer

Complete Answer

0.2668

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