This assignment is due at 11:59 pm (Beijing time) on the date listed on Moodle but you should work on it throughout the week as you finish each Section (the questions are labeled by Section number). Write all work on separate paper,scan, and submit the assignment to Moodle. Be sure to show all steps for full credit.

1. Section 6.1

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. Find the probability that a randomly selected passenger has awaiting time greater than 5.5 minutes.

2. Section 6.2

The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 inches. Use the fact that men’s heights are normally distributed with mean 68.6 inches and standard deviation 2.8 inches.

(a) What percentage of adult males can fit through the door without bending?

(b) Does the door design with a height of 51.6 inches appear to be adequate? Why do you think the engineers didn’t design a larger door?

(c) What doorway height would allow 40% of mentofit without bending?

3. Section 6.2

A professor gives a test and the scores are normally distributed with a mean of 60 and a standard deviation of 12. Suppose she considers curving the scores.

(a)  If she curves by adding 15 points to each grade, what is the new mean and standard deviation?

(b) Is this method of curving fair? Explain why or why not?

(c)  What if she curves the scores by giving grades of B to students who score above the bottom 70% but below the top 10%. Find the numerical limits for a grade of B.