- Transport Canada was investigating accident records to find out how far from their residence people were 2 when they got into a traffic accident. They took the population of accident records from Ontario and measured the distance the drivers were from home when they had their accident in kilometres. The distribution of distances was normally shaped, with µ = 30 kilometers and σ = 8.0 kilometers.
If a random sample 5000 were taken from this dataset, how many of these individuals would you expect were less than 35 kilometers away when they got into an accident? I am asking about the number of individuals from a sample of 5000 that you would be expect to have had their accident when they were less than 35 kilometers away from their home.
Will n be 5000. I was thinking n = 5000 and m = 35 standard error = 8/ square root of 5000 = 8/70.71 = 0.113 then z = 35 - 30/ 0.113 = 44.24. I feel like this is too big to be a z score number. Am i doing it wrong? or am i doing the equation wrong?
You are using standard error where you should be using standard deviation (that is, $\sigma = 8$). You were right to think that $Z>44$ was much too large for the question asked.