(a) With n=12 and p =0.4 find the binomial probability that p(9) by using a binomial probability table. (b) np ¡Ý5, nq¡Ü5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial, is np < 5 or nq < 5 than state the normal approximation and whether it can or cannot be used

To find the binomial probability p(9) with n=12 and p=0.4 using a binomial probability table, you can follow these steps:

(a) Using a Binomial Probability Table:
Step 1: Identify the values of n, p, and x.
In this case, n=12 represents the number of trials, and p=0.4 represents the probability of success for each trial. We want to find p(9), which represents the probability of getting exactly 9 successes.

Step 2: Determine the cumulative probability.
To find p(9), we need to calculate the cumulative probability up to x=9. Cumulative probability means finding the probability of getting x or fewer successes. In this case, we need to find P(x ≤ 9).

Step 3: Locate the corresponding cumulative probability in the binomial probability table.
Using the binomial probability table, find the row that corresponds to the probability of success (p=0.4) and then identify the column for the cumulative probability P(x ≤ 9). The value at the intersection of the row and column will give you the binomial probability.

(b) Normal Approximation to Binomial Distribution:
To determine if the normal distribution can be used as an approximation to the binomial distribution, we need to check if certain conditions are met. The conditions are:
1. np ≥ 5
2. nq ≥ 5

In this case, np = 12 * 0.4 = 4.8, and nq = 12 * (1 - 0.4) = 7.2.

Since both np and nq are less than 5, the normal approximation cannot be used for this scenario.