1. You work with traffic engineers for DOT (the department of transportation) and is in charge of performing measurements and analyzing speeding on a busy road. After measuring the speeds and collected a very large data sample, the speed on that road was found to have a Gaussian distribution with an average of 67 mph and standard deviation of 4 mph. If the highway patrol plans to ticket anyone driving faster than 72 mph, what is the % of drivers that will exceed this limit?

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 %

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

it alot will look like this 4.4

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: