CLT and sample distribution of sample mean

ajc

New Member
#1
On a particular stretch of highway, the state police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Find the probability of obtaining a sample average speed of 66 mph or more if, in fact, the true average speed on that holiday weekend is still 62 mph? μx= σx=
Where do I even start? Im having a hard time understanding what to do? (Using minitab if that is helpful)
 

JesperHP

TS Contributor
#2
You are asked to calculate >>probability of obtaining a sample average<<

so start by defining the sample average

you assume that the sample average is a stochastic variable (a certain function of independent and identical random draws?!)

and in order to calculate the probability of a stoc. var taking on a certain value above some constant a you would usually need to know the distribution...but in this case you should use Central Limit Theorem which under certain assumptions gives an approximate distribution. Here you probably have to use the information that >>the state police know that the average speed is 62 mph with a standard deviation of 5 mph<<

based on these informations you should be able to find the approximate distribution of the sample average and calculate the wanted probability.