Question

A traffic study conducted on an interstate highway shows that vehicle speeds (in mph) are normally distributed with a mean of 61.3 and a standard deviation of 3.3.

a) Sketch the distribution of vehicle speeds. Show 3 steps of standard deviation above and below the mean. b) If a vehicle is randomly checked, what is the probability that its speed is greater than 70? Include a sketch. c) If 5 vehicles are randomly sampled, what is the probability that their mean speed is greater than 70? Include a Sketch.

Answer 1

We are given the distribution here as:

a) The distribution is plotted here as: (Along with the marks for 3 steps above and below mean here as:

b) the probability that the speed is greater than 70 is computed here as:
P(X > 70)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0042 is the required probability here.

This is shown in the plot here as:

c) The probability distribution for the sample means is given here as:

The probability that the sample mean is greater than 70 is computed here as:

Getting it from the standard normal tables, we have here:

Therefore 0 is the required probability here.