Let A be the event that all of a family’s children are the same gender, and let B be the event that the family has at most 1 boy. Assuming the probability of having a girl is the same as the probability of having a boy ( both .5 ), test events A and B for independence if (A) The family has 2 children. (B) The family has 3 children.
Let A be the event that all of a family’s children are the same gender, and let B be the event that the family has at most 1 boy. Assuming the probability of having a girl is the same as the probability of having a boy ( both .5 ), test events A and B for independence if (A) The family has 2 children. (B) The family has 3 children.
Solution Summary: The author explains that the events A and B are dependent on a family having 2 children.
Let
A
be the event that all of a family’s children are the same gender, and let
B
be the event that the family has at most 1 boy. Assuming the probability of having a girl is the same as the probability of having a boy ( both
.5
), test events
A
and
B
for independence if
Problem 3
In their lab, engineer Daniel and Paulina are desperately trying to perfect time travel. But the problem is that
their machine still struggles with power inconsistencies-sometimes generating too little energy, other times
too much, causing unstable time jumps. To prevent catastrophic misjumps into the Jurassic era or the far
future, they must calibrate the machine's power output. After extensive testing, they found that the time
machine's power output follows a normal distribution, with an average energy level of 8.7 gigawatts and a
standard deviation of 1.2 gigawatts.
The Time Travel Safety Board has set strict guidelines: For a successful time jump, the
machine's power must be between 8.5 and 9.5 gigawatts. What is the probability that a randomly
selected time jump meets this precision requirement?
Daniel suggests that adjusting the mean power output could improve time-travel accuracy.
Can adjusting the mean reduce the number of dangerous misjumps? If yes, what should the…
Problem 5 (
Marybeth is also interested in the experiment from Problem 2 (associated with the enhancements for Captain
America's shield), so she decides to start a detailed literature review on the subject. Among others, she found
a paper where they used a 2"(4-1) fractional factorial design in the factors: (A) shield material, (B) throwing
mechanism, (C) edge modification, and (D) handle adjustment. The experimental design used in the paper is
shown in the table below.
a.
Run
A
B
с
D
1
(1)
-1
-1
-1
1
2
a
1
-1
-1
1
3
bd
-1
1
-1
1
4
abd
1
1
-1
1
5
cd
-1
-1
1
-1
6
acd
1
-1
1
-1
7
bc
-1
1
1
-1
abc
1
1
1
-1
paper?
s) What was the generator used in the 2"(4-1) fractional factorial design described in the
b.
Based on the resolution of this design, what do you think about the generator used in the
paper? Do you think it was a good choice, or would you have selected a different one? Explain your
answer in detail.
Not use ai please
Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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