Answer:
The probability that a vehicle passing through this construction zone will exceed the posted speed limit is 0.9332.
Step-by-step explanation:
Let X denote the speeds of vehicles passing through the construction zone.
It is provided that X follows a normal distribution with parameters μ = 46 and σ = 4.
The posted speed limit is of 40 miles per hour.
Compute the probability that a vehicle passing through this construction zone will exceed the posted speed limit as follows:
[tex]P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{40-46}{4})\\\\=P(Z>-1.5)\\\\=P(Z<1.5)\\\\=0.93319\\\\\approx 0.9332[/tex]
Thus, the probability that a vehicle passing through this construction zone will exceed the posted speed limit is 0.9332.
