The New England Insurance Company finds that the ages of motorcyclists killed in crashes are normally distributed with a mean of 26.9 years and a standard deviations of 8.4 years. If we randomly select 1 such motorcyclist, find the probability that he, or she is less then 25 years of age.
What I did was take (1-26.9)/8.4 to get a Z score of -3.08. This got me the probability of .0010. Did I do this correctly?
Another one that I was stuck on was finding the 40th percentile with the data above.
What I did was make a list in my calculator adding/subtracting8.4 from 26.9. My list was 14.8, 23.2, 31.6, 48.4, 56.8, 64.2. Then I did .4 x 6 and got 2.4. Went to my list and took the 3rd number in the list. Not sure if I did this one correctly or not.
Using the data above: if we randomly select 40 such motorcyclists, find the probability that their mean age is less then 25 years. Again, I got the Z score by doing 40-26.9/8.4=1.55. Then got the probability of.9394.
I think you are trying to find a Z score associated with 25 (and then finding the probability to the left of that since you want 25 or less). That would be 25-26.9/8.4 which is not 3.08. I am not sure where the 1 comes from. A z score of -3 would be an extreme outlier (less than one percent of the population) and it is not likely that someone at 25 (with a mean of 26.9) would be this.