Question

Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. 64, p 0.7, and X-40 For n-64, p = 0.7, and X-40, find P(X). P(X)s □ (Round to four decimal places as needed.)

Answer 1

First of all we find the probability using the binomial formula :

We have X = 40 , n = 64 and p = 0.7

We can simply use the Excel function " BINOM.DIST()" to compute the above probability , we get :

Now, we use Normal approximation to estimate the above probability.

We check if

We find :

Mean-np-64 * 0.7 44.8

We can proceed with the Normal Approximation.

Using Standard normal tables or using Excel function " NORMSDIST()" we get :

P(X) = 0.0463

We can see that the Probabilities obtained by binomial formula and Normal approximation are close to each other.