Question

With n=13 and p= 0.7, find the binomial
probability p(9) by using a binomial
probability table. If np> and nq> 5, also
estimate the indicated probability by using the normal distribution as an
approximation to the binomial, if np<5 or
nq<5 then state that the normal approximation cannot be used.

Answer 1

A few hints:

If you use the normal distribution as an approximation, then you will need to find the mean and standard deviation.

mean = np = 13 * 0.7 = 9.1
standard deviation = √npq = √(13)(0.7)(0.3) = 1.65 (rounded)
Note: q = 1 - p

Next step: use z-scores
z = (x - mean)/sd
If x = 9, then
z = (9 - 9.1)/(1.65) = -0.06

Use a z-table to find the probability using the z-score.