Question

if np ≥ 5 and nq ≥ 5, estimate p(more than 7) with n = 11 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution. if np < 5 or nq < 5, then state that the normal approximation is not suitable.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. p(more than 7) =
(round to four decimal places as needed.)
b. the normal distribution cannot be used.

Explanation:

Step1: Calculate np and nq

Given \(n = 11\), \(p=0.6\), then \(q = 1 - p=1 - 0.6 = 0.4\).
\(np=11\times0.6 = 6.6\geq5\) and \(nq=11\times0.4 = 4.4<5\).

Step2: Determine suitability

Since \(nq<5\), the normal - distribution approximation to the binomial distribution is not suitable.

Answer:

B. The normal distribution cannot be used.