Home work 3
Case Weatherhead School of Management OPRE 433 Fall 2014
Homework 3 – SOLUTION
Answer the following questions using JMP wherever you can.
1. Screening at an airport occurs at locations A, B, and C. A handles 50% of the passengers, B handles 30%, and C handles 20%. The detection rates for prohibited items (such as weapons) at the three locations are 0.9, 0.8, and 0.85, respectively.
A. If a passenger at a boarding gate is found with a prohibited item, what is the probability that the passenger was screened at A?
Suppose:
A: Item goes by screening location A
B: Item goes by screening location B
C: Item goes by screening location C
D: Prohibited item is detected at a screening location
So P(A)=0.5, P(B)=0.3, P(C)=0.2, P(D|A)=0.9, P(D|B)=0.8, P(D|C)=0.85
According to Bayes’ Rule: So if a passenger at a boarding gate is found with a prohibited item, the probability that the passenger was screened at A is 0.523.
B. If a passenger at a boarding gate is found with a prohibited item, what is the probability that the passenger was screened at B?
According to Bayes’ Rule: So if a passenger at a boarding gate is found with a prohibited item, the probability that the passenger was screened at B is 0.279.
2. Let X equal the number observed on the throw of a single balanced die.
A. Graph the probability mass function of X. (See the hint after the last question in this homework assignment).
The probability mass function of X can be drawn in JMP as follows:
B. What is
According to the JMP output,
C. What is the standard deviation of X?
As shown in the JMP output,
D. Locate the interval on the abscissa (x-axis) of the graph in part A. What proportion of all values of X fall in this range?
The interval is equivalent to the interval (0.084, 6.916), which means all values of X are located in this range.
3. A piece of electronic equipment has six computer chips. Although two of them are
Homework 3 – SOLUTION
Answer the following questions using JMP wherever you can.
1. Screening at an airport occurs at locations A, B, and C. A handles 50% of the passengers, B handles 30%, and C handles 20%. The detection rates for prohibited items (such as weapons) at the three locations are 0.9, 0.8, and 0.85, respectively.
A. If a passenger at a boarding gate is found with a prohibited item, what is the probability that the passenger was screened at A?
Suppose:
A: Item goes by screening location A
B: Item goes by screening location B
C: Item goes by screening location C
D: Prohibited item is detected at a screening location
So P(A)=0.5, P(B)=0.3, P(C)=0.2, P(D|A)=0.9, P(D|B)=0.8, P(D|C)=0.85
According to Bayes’ Rule: So if a passenger at a boarding gate is found with a prohibited item, the probability that the passenger was screened at A is 0.523.
B. If a passenger at a boarding gate is found with a prohibited item, what is the probability that the passenger was screened at B?
According to Bayes’ Rule: So if a passenger at a boarding gate is found with a prohibited item, the probability that the passenger was screened at B is 0.279.
2. Let X equal the number observed on the throw of a single balanced die.
A. Graph the probability mass function of X. (See the hint after the last question in this homework assignment).
The probability mass function of X can be drawn in JMP as follows:
B. What is
According to the JMP output,
C. What is the standard deviation of X?
As shown in the JMP output,
D. Locate the interval on the abscissa (x-axis) of the graph in part A. What proportion of all values of X fall in this range?
The interval is equivalent to the interval (0.084, 6.916), which means all values of X are located in this range.
3. A piece of electronic equipment has six computer chips. Although two of them are