IE3302 HW#6
Due by end of day (11:59pm) Fri 3/19
To be worked individually. Calculated values may be given in fraction or decimal form; if in
decimal form must be rounded to 4 decimal places. 100pt assignment. To be worked
individually. All problems to be submitted in order, in a single Word or PDF document, to the
Hw#6 Moodle dropbox. If handwritten & scanned, or use handwritten with digital ink, ensure
that all solutions are legible before submitting. Work must be shown for credit. Book problems
are 8pt each, other problems 15pt each.
1. Book problem 6.3
2. Book problem 6.7
3. Book problem 6.12
4. A work process takes X~Norm(58,11) minutes.
a. Take an observation and get X=56.5. Z?
b. Pr(X<58 or X>60)?
c. X0.3?
5. Suppose in the population that heights are ~NORM(68,15) inches. How high should a
door opening be such that 98% of the population will fit through it with at least 4” of
clearance above their heads?
6. Book problem 6.22
7. Book problem 6.36
8. At College Drive and I-10, cars run the red lights at the intersection at a rate of 4 per
hour.
a. What is the probability of no more than 5 cars running a red light in any 2-hour
period?
b. What is the probability that the time between any two cars running a red light
will be > 30 minutes?
c. The last person to run a red light occurred at 10:15am this morning. It is
currently 11am. What is the probability that the next person to run a red light
will not be until after 11:30am?
d. What is the median (50th percentile) time between cars running a red light?
e. The intersection has a red light camara. If the fine for a running a red light is
$117, and 60% of people fined actually pay the fine, how much ticket revenue is
generated per hour on average?
9. Breakdowns of an older car follow T~Weib(t; =1.8, =100 days).
a. Indicate whether the failure rate of the car is increasing, decreasing, or constant
with time, and the reason for your conclusion
b. Pr(T≤ 20 days)?
