z score and probability

Question

suppose a bell shaped distribution, with a mean of 70 mph and a std dev of 8 mph. Calculate the Z score for someone traveling 95 mph. Is it likely to see someone going this fast? We must use Excel and the directions state that we must use the appropriate function to justify our response and give the EXACT probability.

I am a little confused about this question because it does not say the car is traveling greater than, or less than. The way I interpret this question: it is asking what is the likelihood of seeing someone driving AT exactly 95 mph. Am I wrong?

At any rate, I have no idea how to solve this using excel. Doing it with STANDARDIZE gives me a 3.125 z score and a probability of 99% which makes no sense!

Please do your best to explain the answer as I really want to learn stats correctly

Answer 1

You have calculated the z score correctly, it is (95-70) / 8 = 3.125  

 

99% is the probability that someone is traveling less than 95 mph.  This question is asking you to find the probability that someone is going faster than 95 mph, which is 1 - 0.99 = 0.01 = 1%.  

 

By the way, for a z score of 3.125 I get P = 0.9991, which means that 1 - P = 0.0009 = 0.09% is the probability that someone is going faster than 95 mph.  

 

When you have a continuous distribution (that is, the values can be any real number like 95.1 mph or 94.78 mph or 95.5324 mph) it doesn't really make sense to ask for the likelihood that someone is going EXACTLY a given speed.  The Z score lookup will only give you the probability that an event is less than your given value.  If you want to find the probability that an event is greater than your given value you subtract this probability from 1.