SOLUTION: Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why

Algebra ->  Probability-and-statistics -> SOLUTION: Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why       Log On


   

Question 879271: Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Thank you for help, I need to know how it is figured out please
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Convert the raw score of xbar = 115 to a z score

z = (xbar - mu)/(sigma/sqrt(n))

z = (115 - 100)/(15/sqrt(3))

z = 1.73205080756888

z = 1.73

This z score is within 3 standard deviations of the mean, so it is not unusual at all.