What is the probability that it will take a resident of this city between 20 and 40 minutes to travel to work? with a mean of 38.3

Question

 What is the probability that it will take a resident of this city between 20 and 40 minutes to travel to work? the mean is 38.3

Answer 1

20 mins is 18.3 below the mean, and 40 mins is 1.7 mins above the mean. We don’t know the standard deviation. Let’s assume the SD is roughly the square root of the mean, that is, about 6, then we can work out a probability. -18.3/6=-3.05 and 1.7/6=0.28 approx. We can use these as Z scores, Z1=-3.05 and Z2=0.28.

From these we get two probabilities: for Z1, p1=1-N(3.05)=1-0.9989=0.0011. For Z2, p2=0.6103.

p2-p1=0.6092, or about 0.61.

However, we will get different results if we change the SD. Let SD=8 mins.

This time Z1=-2.29 and Z2=0.21. p1=0.011 and p2=0.583, p2-p1=0.57 approx.

So we can conclude from these examples that the probability is about 60%.