An article stated, \"Surveys tell us that more than half of America\'s college g

Question

An article stated, "Surveys tell us that more than half of America's college graduates are avid readers of mystery novels." Let p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion p that is based on a random sample of 235 college graduates.

(a) If p = 0.5, what are the mean value and standard deviation of p? (Round your answers to four decimal places.)

If p = 0.6, what are the mean value and standard deviation of p? (Round your answers to four decimal places.)

(b) Calculate P(p 0.6) for p = 0.5. (Round your answer to four decimal places.)
  

Explanation / Answer

a)
Mean ( np ) =117.5
Standard Deviation ( npq )= 235*0.5*0.5 = 7.6649

b)
Mean ( np ) =141
Standard Deviation ( npq )= 235*0.6*0.4 = 7.51

c)
Proportion ( P ) =0.5
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.5*0.5/235)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.6) = (0.6-0.5)/0.0326
= 0.1/0.0326= 3.0675
= P ( Z <3.0675) From Standard Normal Table
= 0.9989                  

P(X >= 0.6) = 1 -P(X < 0.6) = 1 - 0.9989 = 0.0011

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