A traffic officer has a concealed radar unit that she uses to measure the speed of traffic crossing a bridge. She finds that the mean speed is 84km/h and the standard deviation is 5km/h.
a) What probability distribution is most likely to model the speed of the traffic crossing the bridge? Explain why you made your choice and give any parameter(s) for your distribution.
b) If the speed limit on the bridge is 90km/h, find out how many out of 200 cars she would expect to find to be breaking the limit.

2. Originally Posted by Kiwigirl
A traffic officer has a concealed radar unit that she uses to measure the speed of traffic crossing a bridge. She finds that the mean speed is 84km/h and the standard deviation is 5km/h.
a) What probability distribution is most likely to model the speed of the traffic crossing the bridge? Explain why you made your choice and give any parameter(s) for your distribution.
b) If the speed limit on the bridge is 90km/h, find out how many out of 200 cars she would expect to find to be breaking the limit.
a)I do not understand this one, I just understand that as normal distribution.

b)
You need to find $P(90\geq x)$.
You need to find how many standard deviations over you moved. Since the mean is 84 and standard deviation is 5 how many standard deviations to you move up to get to 90? Notice that 1 standard deviation up gives 84+5=89 which is too little, while 2 standard deviation gives 84+2x5=94 which is too much. Thus, we need to solve,
$84+5z=90$ solving we have, $z=1.2$ now we need to look up the precentage on distribution tables, which is .3849. Thus, we have,
$P(84\leq x\leq 90)\approx .3849$
Also, since normal distribution is symetrrical we have,
$P(x\leq 84)=.50$
Thus, that leaves over,
$P(90\geq x)\approx 1-.50-.3849\approx .1151$.
Thus, since there were 200 we have approximately 11% of it which is 23.