Question

Thank you in advance!

The District of Columbia Police Department are gathering highway speed data along a section of the Capital Beltway to determine if the current speed limit is being followed. A radar speed detection device is used to measure the speeds of cars on the expressway. The speeds are normally distributed. The speed gun captures the speed of 6 vehicles as 80mph, 70mph, 100mph, 70mph, 80mph and 80mph.

1. What is the mean of the speeds on the expressway captured by the speed gun?
2. Given the speeds captured by the speed gun, what is the standard deviation for speeds along the highway?
3. Sketch a normal distribution diagram to illustrate the mean and standard deviation, indicating clearly the mean and the speeds within one, two and three standard deviations of the mean.
4. Find the probability that a vehicle is traveling faster than 110mph.
5. The radar gun captures the speeds of a population of 1000 vehicles traveling the expressway. Calculate the number of vehicles expected to be traveling less than 70mph.

Answer 1

The solution to the statistics and probability problem is given below