1. I want to know how my grade on the midterm compares to the rest of my classmates. My

professor tells me that the grades are normally distributed, there was an average score of 83

and a standard deviation of 8. What percentage of students received a higher score on the

midterm than me if I scored a 92? What did the top 15% of students earn? What did the bottom

15% of students earn?

2. A local hospital is examining the length of hospital stays for its patients. They find that the

length of stays for their patients is normally distributed. The mean hospital stay is 200 hours and

the standard deviation is 75 hours. What percentage of patients had a hospital stay longer than

300 hours? What percentage of patients had a stay less than 75 hours? What length of stay (in

hours) would a patient need to be considered in the top 25%? What would the length of the

stay need to be (in hours) to be in the bottom 10%?

3. In our random sample of 50 Iowa residents, we find an average of 10 connected devices in

each home (TV’s, computers, cell phones, lights, etc.). The standard deviation of all Iowa

residents is 2. Estimate the population mean using a 99% confidence interval.

4. A researcher interested in the age people begin smoking knows that the standard deviation for

United States smokers is 1.75 years, but he does not know the average age of onset. In order to

estimate the average age of onset, he randomly selects 35 smokers who have an average onset

age of 15. Using a 95% confidence interval, estimate the national average age of onset for

smokers.