Question 1057713
Because the sample size is > 30, we can assume a normal distribution
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The mean of the population is the mean of the sample, that is, 0.415
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The sample standard deviation is square root ( 0.415 * (1-0.415) / 200 ) = 0.0348
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a) 75/200 = 0.375
z-value = ( 0.375 - 0.415 ) / 0.0348 = -1.1494 approx -1.15
lookup z-value in table of z-values to find the associated probability(Pr)
Pr ( X < 75 ) = 0.1251
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b) 80/200 = 0.4 and 90/200 = 0.45
Pr ( 80 < X < 90 ) = Pr ( X < 90 ) - Pr ( X < 80 )
z-value for 80 is ( 0.4 - 0.415 ) / 0.0348 = -0.431 approx -0.43
z-value for 90 is ( 0.45 - 0.415 ) / 0.0348 = 1.0057 approx 1.01
Pr ( 80 < X < 90 ) = 0.8438 - 0.3336 = 0.5102
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c) 70/200 = 0.35
Pr ( X < 70 or X > 90 ) = Pr ( X < 70 ) + ( 1 - Pr ( X < 90 )
z-value for 70 is ( 0.35 - 0.415 ) / 0.0348 = -1.8678 approx -1.87
Pr ( X < 70 or X > 90 ) = 0.0307 + 0.1562 = 0.1869
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