Assume that a population's IQ 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 35 to be 115 or more? While we can use the rule-of-thumb that a sample whose standard deviation is greater than 2 standard deviation is an unusual event I suggest that a preferred measure to use is a probability of less than or equal to 0.05. For a discussion on this I recommend you see p. 105 in the textbook and pay particular attention to the paragraph at the foot of the page
Interpreting Normal Distributions:
1)What if the size of sample was decreased to 5? Would a sample mean of 115 or more be considered unusual? Why or why not?
2)Why is the Central Limit Theorem used?
3)Consider situations in your work or home that could be addressed through a continuous probability distribution. Describe the situation and the variables, and determine whether the variables are normally distributed or not. How could you change these to a normally distributed data set?