The speeds of vehicles on a highway with speed limit 100 km/h are normally distributed with mean 114 km/h and standard deviation 8 km/h. (Round your answers to two decimal places.) ((a) What is the probability that a randomly chosen vehicle is traveling at a legal speed?

%

(b) If police are instructed to ticket motorists driving 125 km/h or more, what percentage of motorist are targeted?

%

a)

And we can find this probabiliy using the normal standard table or excel and we got:

So then we expect about 4%

b)

And we can find this probabiliy using the complement rule and the normal standard table or excel and we got:

So then we expect about 8.5%

Step-by-step explanation:

Part a

Let X the random variable that represent the speeds of vehicles, and for this case we know the distribution for X is given by:

Where and

We want to find this probability  (legal speed)

We can use the z score given by:

If we apply this formula to our probability we got this:

And we can find this probabiliy using the normal standard table or excel and we got:

So then we expect about 4%

Part b

And we can find this probabiliy using the complement rule and the normal standard table or excel and we got:

So then we expect about 8.50%

3

step-by-step explanation: