Question 977868
This is a problem using the Sampling Distribution of the Proportion
The mean of the sample is .73
standard deviation of the sample is square root(PQ/n) where P=0.73, Q=0.27 and n =69
standard deviation of the sample is square root(0.73*0.27/69) = 0.053446438
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mean(p) = 0.73 and std dev(p) = 0.05
40/69 = 0.579710145 approx 0.58
46/69 = 0.666666667 approx 0.67
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a) Probability(P) ( 40 < X < 46 ) = P ( X < 46) - P ( X < 40 )
z-value for 46 is (0.67 - 0.73) / 0.05 = -1.2 and
P ( X < 46 ) = 0.1151
z-value for 40 is (0.58 - 0.73) / 0.05 = -3 and
P ( X < 40 ) = 0.0013
therefore
Probability(P) ( 40 < X < 46 ) = 0.1151 - 0.0013 = 0.1138
b) P ( X < 40 ) = 0.0013