Quality control. A manufacturing process produces, on average, 5 defective items out of 100 . To control quality, each day a random sample of 6 completed items is selected and inspected. If success on a single trial (inspection of 1 item) is finding the item defective, then the inspection of each of 6 items in the sample constitutes a binomial experiment. For the binomial distribution, (A) Write the probability function. (B) Construct a table. (C) Draw a histogram. (D) Compute the mean and standard deviation
Quality control. A manufacturing process produces, on average, 5 defective items out of 100 . To control quality, each day a random sample of 6 completed items is selected and inspected. If success on a single trial (inspection of 1 item) is finding the item defective, then the inspection of each of 6 items in the sample constitutes a binomial experiment. For the binomial distribution, (A) Write the probability function. (B) Construct a table. (C) Draw a histogram. (D) Compute the mean and standard deviation
Solution Summary: The author explains that the probability function is given if a machine produces 5 defective items out of 100 items.
Quality control. A manufacturing process produces, on average,
5
defective items out of
100
. To control quality, each day a random sample of
6
completed items is selected and inspected. If success on a single trial (inspection of
1
item) is finding the item defective, then the inspection of each of
6
items in the sample constitutes a binomial experiment. For the binomial distribution,
Cycles to
failure
Position in
ascending
order
0.5
f(x))
(x;)
Problem 44
Marsha, a renowned cake scientist, is trying to determine how long different cakes can survive intense fork attacks before collapsing into crumbs.
To simulate real-world cake consumption, she designs a test where cakes are subjected to repeated fork stabs and bites, mimicking the brutal
reality of birthday parties. After rigorous testing, Marsha records 10 observations of how many stabs each cake endured before structural failure.
Construct P-P plots for (a.) a normal distribution, (b.) a lognormal distribution, and (c.) a Weibull distribution (using the information included in the
table below). Which distribution seems to be the best model for the cycles to failure for this material? Explain your answer in detail.
Observation
Empirical
cumulative
Probability distribution
Cumulative distribution
Inverse of cumulative
distribution F-1 (-0.5)
F(x))
(S)
n
4
3
1
0.05
9
5
2
0.15
7
7
3
0.25
1
10
4
0.35
3
12
5
0.45
Normal…
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.
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License