Question

State police believe that 68% of the drivers drive above the speed limit on the freeway. Driving behavior of a random sample of 110 drivers were observed with hidden cameras. What is the probability that in that sample more than 73% of the drivers crossed the speed limit? Answer to 4 decimal places.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     μp=	0.6800
sample size       =n=	110

std error of proportion=σp=√(p*(1-p)/n)=0.0445

probability that in that sample more than 73% of the drivers crossed the speed limit :

probability =P(X>0.73)=P(Z>(0.73-0.68)/0.045)=P(Z>1.12)=1-P(Z<1.12)=1-0.8686=0.1314

(please try 0.1306 if this comes wrong)