In a Marist College poll of 1004 adults 291 chose profession

In a Marist College poll of 1004 adults, 291 chose professional athelete as their dream job. Assume that 25% of adults consider beinga professional athelete as their dream job.

A. The result of the 291 is more than 25% of 1004, so find the probabilility that among 1004 random adults, 291 or more consider being a professional athlete was their dream job.

B. If the values of 25% is correct, is the result of 291 unusually high?

C. Does the result suggest that the rate is great than 25%?

Solution

a)

Here,

mean = np = 1004*0.25 = 251
standard deviation = sqrt(np(1-p)) = sqrt(1004*0.25*(1-0.25)) = 13.72042273

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    290.5      
u = mean =    251      
          
s = standard deviation =    13.72042273      
          
Thus,          
          
z = (x - u) / s =    2.878920043      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.878920043   ) =    0.001995197 [ANSWER]

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b)

Yes, it is unusually high, as its probability is low.

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c)

Yes, because the probability makes it hard to believe that this just happened by chance.