Introduction to probability?

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Suppose that 75 percent of the people in a certain metropolitan area live int he city and 25 percent of the people live in the suburbs. If 1200 people attending a certain concert represent a random sample from the metropolitan area, what is the probability that the number of people from the suburbs attending the concert will be fewer than 270?
 
p = 25% = 0.25
q = 1 - p = 1 - 0.25 = 0.75
n = 1200
Standard deviation = sq rt npq
= sq rt 1200*0.25*0.75
= sq rt 225
= 15
Observed number of people from the suburbs attending the concert = X = 270
Expected number of people from the suburbs attending the concert = Mean = np = 0.25* 1200 = 300
z =( X - Mean)/S.D
z = (270 - 300)/15
= - 30/15 = - 2
Area under the standard normal curve corresponding to z = - 2 is 0.4772
Required probability = 0.5000 - 0.4772 = 0.0228 or 2.28%
 
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