Answer:
The % of drivers that will exceed this limit is 10.56 %
Step-by-step explanation:
Let's start defining the random variable :
: '' The speed on that road ''
We know that can be modeled with a Gaussian distribution ⇒
~ ( μ , σ )
Where ''μ'' is the mean and ''σ'' is the standard deviation. Given that the average speed and the standard deviation of the problem are known we write :
~
We are asked about (which is the % of drivers that will exceed this limit).
To find this probability we are going to make a standardization of the variable (also called a change of variables).
We are going to substract the mean to and then divide by its standard deviation :
P [(X-μ) / σ > (72 - μ) / σ] (I)
The new variable [(X - μ) / σ] is called Z.
Z can be modeled as
~
⇒ Replacing in (I) the values of the mean and the standard deviation :
=
The convenience of this is that we can find the probabilities of Z (which is a N(0,1) ) in any table on internet ⇒
Looking at any table we will find that ⇒
= 10.56 %
We find that the % of drivers that will exceed this limits is 10.56 %