Question

Assume the speed of vehicles along a stretch of road has an approximately normal distribution with a mean of 61 mph and a standard deviation of 6 mph. The current speed limit is 55 mph. What is the proportion of vehicles less than or equal to the speed limit?

A) Approximately 0.1587

B) Approximately 0.8413

C) Approximately 0.5

D) Approximately 0.025

Answer 1

The proportion of vehicles less than or equal to the speed limit is found by calculating the Z-score for 55 mph and using the standard normal distribution to find the cumulative probability. The correct answer is A) Approximately 0.1587.

Step-by-step explanation:

To determine the proportion of vehicles less than or equal to the speed limit, we can use the standard normal (Z) distribution since the problem states that the speeds are normally distributed. First, we find the Z-score for the speed limit:

Z = (X - μ) / σ = (55 mph - 61 mph) / 6 mph = -6 mph / 6 mph = -1

Then, using a Z-table or a standard normal distribution calculator, we find the cumulative probability for Z = -1, which represents the proportion of vehicles traveling at or below 55 mph. The cumulative probability corresponding to Z = -1 is approximately 0.1587.

Therefore, the correct answer is:

A) Approximately 0.1587