Question

A construction zone on highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 miles per hour and a standard deviation of 4 miles per hour. What is the probability that a vehicle passing through this construction zone will exceed the posted speed limit.( round your answer to four decimal places

Answer 1

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:

$P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{40-46}{4})\\\\=P(Z>-1.5)\\\\=P(Z$

Thus, the probability that a vehicle passing through this construction zone will exceed the posted speed limit is 0.9332.