SOLUTION: the speed of motorists on a highway is normally distrubuted with a mean of 120km/h and variance of 240. If the metro-police wants to stop the 5% fastest motorists, what is the cut-

Question 984758: the speed of motorists on a highway is normally distrubuted with a mean of 120km/h and variance of 240. If the metro-police wants to stop the 5% fastest motorists, what is the cut-off speed so that all cars which travel at a speed faster than the cut-off speed will be stopped
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I want the standard deviation, which is sqrt (variance)=sqrt(240)=15.49
;
The fastest 95% of the motorists will have a z-score greater than or equal to 1.645.
z=(x-mean)/sd
1.645=(speed-average/sd
1.645=(x-120)/15.49
multiply both sides by 15.49
26.14=x-120
x=146.14 km/h or faster than 147 km/h rounding upward.
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