A particular program say program A previously drew 30 of th

A particular program, say, program A, previously drew 30 % of the television audience. To determine if a recent rescheduling of the programs on a competing channel has adversely affected the audience of program A, a random sample of 400 viewers is to be asked whether or not they currently watch this program. If the percentage of viewers watching program A has not changed, what is the probability that fewer than 106 out of a sample of 400 will be found to watch the program?

Solution

We first get the z score for the critical value:          
          
x = critical value =    104.5      
u = mean = np =    120      
          
s = standard deviation = sqrt(np(1-p)) =    9.16515139      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -1.691188649      
          
Thus, the left tailed area is          
          
P(z <   -1.691188649   ) =    0.045400389 [ANSWER]