Assume a binomial probability distribution with n40 and p055

Assume a binomial probability distribution with n=40 and p=0.55. Compute the following: The mean and standard deviation of the random variable. The probability that x is between 15 and 25, inclusive.

Solution

Normal Distribution
a)
Mean ( np ) = 22
Standard Deviation ( npq )= 40*0.55*0.45 = 3.1464
Normal Distribution = Z= X- u / sd                   
b)
To find P( X > a or X < b ) = P ( X > a ) + P( X < b)
P(X < 15) = (15-22)/3.1464
= -7/3.1464= -2.2248
= P ( Z <-2.2248) From Standard Normal Table
= 0.013
P(X > 25) = (25-22)/3.1464
= 3/3.1464 = 0.9535
= P ( Z >0.953) From Standard Normal Table
= 0.1702
P( X < 15 OR X > 25) = 0.013+0.1702 = 0.1832                  
P( 15 < = X < = 25) = 1 - P( X < 15 OR X > 25) = 1 - 0.1832 = 0.8168