It is known that roughly 2/3 of all human beings have a dominant right foot or e

Question

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 130 kissing couples, both people in 84 of the couples tended to lean more to the right than to the left. (Use = 0.05.) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 130 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.)

Explanation / Answer

We first get the z score for the critical value:          
          
x = critical value =    84 (Given)      
u = mean = np =    130 *(2/3) = 86.66666671      
          
s = standard deviation = sqrt(np(1-p)) = sqrt(130*(2/3)(1-2/3)) =   5.374838498      
          
Thus, the corresponding z score is          
          
z = (x-u)/s = (84 - 86.66666671)/5.374838498 =   -0.50
          
Thus, the left tailed area is          
          
P(z <   -0.50   ) =    0.3099

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

P = 2(0.3099) = 0.6198

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