It is known that roughly 23 of all human beings have a domin

It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 133 kissing couples, both people in 85 of the couples tended to lean more to the right than to the left.

(a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 133 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to three decimal places.)

Solution

We first get the z score for the critical value:          
          
x = critical value =    85 (Given)      
u = mean = np =    133 *(2/3) = 88.6666667     
          
s = standard deviation = sqrt(np(1-p)) = sqrt(133*(2/3)(1-2/3)) =   5.436502143    
          
Thus, the corresponding z score is          
          
z = (x-u)/s = (85 - 88.66666671)/5.436502143 =   -0.67
          
Thus, the left tailed area is          
          
P(z <   -0.67 ) =    0.2500

As it is two tailed, we multiply this by 2,

P = 2(0.2500) = 0.5000