Question

It has been reported that 45% of all college students use Twitter If we survey a simple
random sample of n = 225 college students and ask if they use Twitter, the percentage who
say “yes” will vary if the sampling method is repeated. In fact, the sampling distribution of
the percentage who say they use Twitter, in many samples of size n = 225, will be Normal in
shape, with mean (or center) of 45% and standard deviation of 3.3%. Based on this
information, we know that the probability of obtaining a sample (of size n = 225) where
39% or fewer students say they use Twitter is

Answer 1

population proportion ,p=   0.45                          
n=   225                          
                              
std error , SE = √( p(1-p)/n ) =    0.0332                          
                              
sample proportion , p̂ =   0.39                          
Z=( p̂ - p )/SE= (   0.390   -   0.45   ) /    0.033   =   -1.809  
P ( p̂ <    0.390   ) =P(Z<( p̂ - p )/SE) =                      
                              
=P(Z <    -1.809   ) =    0.0352                   (answer)

excel formula for probability from z score is =NORMSDIST(Z)