An elevator is designed to hold 1150 kg. The mass of males is normally distributed with a mean of 85.5 kg and a standard deviation of 17.6. For females, the mean is 77.6 kg with a standard deviation of 20.8. Assume the general population is split evenly between the two.

11. What is the probability that a woman weighs less than 70 kg.

12. What is the 75th percentile of female weight?

13. If the elevator were installed in a female dormitory, on average, how many women could the elevator hold before it exceeds the design capacity?

14. What is the probability that 20 women could fit in the elevator without exceeding its capacity?

15. A sensor is installed on the elevator to indicate whenever the load is near capacity. The sensor is set to activate when the elevator mass is greater than 1100 kg. However, it is not perfectly accurate and has a standard deviation of 10 kg. What is the probability that 11 women in the elevator will cause the sensor to activate?

16. The dormitory is made co-ed with both male and female occupants. Now how many people could the elevator hold before exceeding design capacity?

17. In the new co-ed dormitory, how often is the design capacity exceeded with only 11 people?