Determine if the outcome is unusual. Consider as unusual any result that differs

Question

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than muminus2sigma or greater than muplus+2sigma. According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 979979 of the 2500 televisions are tuned to "Eyewitness News"?

Explanation / Answer

Here, n = 2500, p = 0.36.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 979/2500 =   0.3916      
u = mean = p =    0.36      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.0096      
          
Thus,          
          
z = (x - u) / s =    3.291666667      
          
As |z| > 2, then YES, THIS IS UNUSUAL. [ANSWER]

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