Evaluate the expression 4(x - 3) + 7 using x=2

a.  22,7% of the vehicles are going less than or equal to 65 mph.

b. 0,4% of the vehicles are going less than 50 mph.

c. if the speed limit would be 81.25 mph, aproximately 10% of vwhicles would be over that speed.

Step-by-step explanation:

Part A.

The portion of vehicles with speed less than or equal to 65 mph, could be estimate by the probability of X≤65. If the speed follow a normal distribution, the probability is:

According to normal distribution table,

It means that 22,7% of the vehicles are going less than or equal to 65 mph.

Part B.

The portion of vehicles with speed less than 50 mph, could be estimate by the probability of X<50. If the speed follow a normal distribution, the probability is:

According to normal distribution table,

It means that 0,4% of the vehicles are going less than 50 mph.

Part C.

1. Find Z-value

The portion of vehicles that will be over the speed limit, could be expressed like:

When, SL is the speed limit in a santdard normal distribution.

Using the normal distribution table, we will find the Z- value corresponding to probability of 0.9

We find that Z- value for p=0.9 is 1.282

2. Transform Z in X

It's necessary transforming Z-value in X, by the equation:

Then:

It means that if the speed limit would be 81.25 mph, aproximately 10% of vwhicles would be over that speed.

Part D.

The distribution doesn't seem to be symmetric, the values are not distributed symmetrically around the mean.