20 of all dragons can breath fire Based on a random sample o

20% of all dragons can breath fire. Based on a random sample of 1,000 dragons, answer the following: What is the probability that in the sample of 1,000 dragons that the proportion that can breathe fire is less than 18% ? PLease help ive been trying to firgure this problem out all day

Solution

Here, the standard deviation of p is given by

s(p) = sqrt(p(1-p)/n) = sqrt(0.20*(1-0.20)/1000) = 0.012649111

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.18      
u = mean =    0.2      
          
s = standard deviation =    0.012649111      
          
Thus,          
          
z = (x - u) / s =    -1.581138785      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.581138785   ) =    0.056923154 [ANSWER]