Ten percent of the population is lefthanded A class of 100 s

Ten percent of the population is left-handed. A class of 100 students is selected. Convert the binomial probability P(x > 12) to a normal probability by using the correction for continuity.

Solution

Here,

Mean = n p = 100*0.10 = 10

Standard deviation = sqrt(np(1-p)) = sqrt(100*0.1*(1-0.1)) = 3

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    11.5      
u = mean =    10      
          
s = standard deviation =    3      
          
Thus,          
          
z = (x - u) / s =    0.5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.5   ) =    0.308537539 [ANSWER]