If $n p \geq 5$ and $n q \geq 5$, estimate $P($ fewer than 5 ) with $n=13$ and $p=0.5$ by using the normal distribution as an approximation to the binomial distribution; if $n p< 5$ or $n q< 5$, 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. $P($ fewer than 5$)=$
(Round to four decimal places as needed.)
B. The normal approximation is not suitable.

Step 1 ：The problem is asking to estimate the probability of getting fewer than 5 successes in a binomial distribution with parameters \(n=13\) and \(p=0.5\) using the normal approximation. The normal approximation to the binomial distribution is suitable when both \(np\) and \(nq\) are greater than or equal to 5. Here, \(np = 13*0.5 = 6.5\) and \(nq = 13*0.5 = 6.5\), so the normal approximation is suitable.

Step 2 ：The mean of the binomial distribution is \(np = 6.5\) and the standard deviation is \(\sqrt{npq} = \sqrt{13*0.5*0.5} = 1.8028\).

Step 3 ：We want to find \(P(X<5)\), but since we are using a continuous distribution to approximate a discrete one, we use the continuity correction and find \(P(X<4.5)\) instead.

Step 4 ：To standardize, we subtract the mean and divide by the standard deviation, getting \(Z = \frac{4.5 - 6.5}{1.8028}\).

Step 5 ：We can then look up this Z-score in the standard normal table to find the probability.

Step 6 ：Final Answer: The probability of getting fewer than 5 successes is approximately \(\boxed{0.1336}\).