Statistics Canada reports that one in four people 15 years o

Statistics Canada reports that one in four people 15 years of age or older volunteers some of his or her time. If this figure holds for the entire population and if a random sample of 159 people 15 years of age or older is taken, what is the probability that more than 44 of those sampled do volunteer work?

Round the value of p to 2 decimal places. Round the value of to 3 decimal places. Round the value of z to 2 decimal places. Round your answer to 4 decimal places.

Solution

We first get the z score for the critical value:          
          
x = critical value =    44.5      
u = mean = np =    39.75      
          
s = standard deviation = sqrt(np(1-p)) =    5.460082417      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.87      
          
Thus, the left tailed area is          
          
P(z <   0.87   ) =    0.1922 [ANSWER]