One in four college students is aged 30 or older Say you sam

One in four college students is aged 30 or older. Say you sample 200 students from your college, recording X, the number of students age 30 or over. If there are 35 students in your sample over age 30 would you be willinging to assume that the 25% figure is reprentative on your campus?

Solution

The mean number we might expect is 200*0.25 = 50 students 30 or over.

Thus, getting a 35 is lower than expected. How rare is this?

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    200      
p = the probability of a success =    0.25      
x = the maximum number of successes =    35      
          
Then the cumulative probability is          
          
P(at most   35   ) =    0.007288409
          
As this is very rare, then we might no assume the the 25% figure is representative on our campus. [ANSWER]