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. nequals62​, pequals0.3​, and Xequals8

Answer 1

If X follows Binomial distribution with n and p then

                      x = 0,1,2,...........,n

n!= 1*2*3*4*...........*n

Here n = 62 , p = 0.3

                   

                      

                     

                     = 0.00096               (Round to 5 decimal)

P(X = 8) = 0.00096

Here n * p = 62 * 0.3 = 18.6 > 5

         n * (1-p) = 62 * 0.7 = 43.4 > 5

Here Conditions are satisfied.So we can use normal approximation here.

Since Binomial is discrete and normal is continuous, a continuity correction factor must be applied when using normal approximation to binomial distribution.

But for continuous distribution P(X=a) is always zero.

So P(X = 8) = 0