An article stated Surveys tell us that more than half of Ame

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.)
  

Solution

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