Quiz #4
Semester 041
Instructor: Dr. Mohammad H. Omar
Stat319: Introduction to Probability & Statistics for Engineers and Scientists
Name:_______________________ ID#:______________ Section: 2 (8-8.50am) 4(9-9.50am)
Directions: There are two questions you must answer to obtain a total of 10 points for this quiz.
The last question is optional and is provided as a bonus.
1. [6 pts]Miyamura (1982) modeled the lifetimes of the electromagnetic valve used for starting the
idle-up actuator of an air conditioner by an exponential distribution with a rate of 0.05 failure
per million revolutions. Consider a randomly selected electromagnetic valve.
(a)
(b)
(c)
(d)
Find the probability that this valve fails within the first half million revolutions
Find the probability that this valve lasts longer than 3 million revolutions
Find the expected time to failure for this valve
Find the standard deviation for the time to failure for this valve
2. [4 pts] The length of an injected-molded plastic case that holds magnetic tape is normally
distributed with a length of 90.2 millimeters and a standard deviation of 0.1 millimeters.
(a)
(b)
What is the probability that a part is longer than 90.3 millimeters?
If a total of 5% of the shortest and the longest parts are scrapped, what are the minimum
and maximum acceptable lengths of the injected-molded plastic case?
3. [Bonus - 6 pts]The manufacturing of semiconductor chips produces 2% defective chips. Assume
the chips are independent and that a lot contains 1000 chips.
(a)
(b)
(c)
Find the probability that no chip is defective
Approximate the probability that more than 25 chips are defective.
Approximate the probability that between 20 and 30 chips are defective.
Answers
1a)
1b)
1c)
-e-0.05x evaluated between 0 and ½ =0.02469
-e-0.05(3) = 0.860708
 = 1/= = 20
1d)  =1/ =  = 20
2a)
0.15866
2b)
min=90.0355 & max=90.3645
3a)
0.129
3b)
0.488