2-23 Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is inspected and found to be acceptable. At this point, what is the posterior probability that the lathe tool is properly adjusted?
Answers
Answer:
The posterior probability that the lathe tool is properly adjusted is 94.7%
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In your problem we have that:
-A is the probability that the part chosen is found to be acceptable.
The problem states that the probability its lathe tool is properly adjusted is 0.8. When it happens, there is a 0.9 probability that the parts produced pass inspection. There is also a 0.2 probability of the lathe is out of adjustment, when it happens the probability of a good part being produced is only 0.2.
So, P(A) = P1 + P2 = 0.8*0.9 + 0.2*0.2 = 0.72 + 0.04 = 0.76
Where P1 is the probability of a good part being produced when lathe tool is properly adjusted and P2 is the probability of a good part being produced when lathe tool is not properly adjusted.
- P(B) is the the probability its lathe tool is properly adjusted. The problem states that P(B) = 0.8
P(A/B) is the probability of A happening given that B has happened. We have that A is the probability that the part chosen is found to be acceptable and B is the probability its lathe tool is properly adjusted. The problem states that when the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. So P(A/B) = 0.9
So, probability of B happening, knowing that A has happened, where B is the lathe tool is properly adjusted and A is that the part randomly chosen is inspected and found to be acceptable is:
The posterior probability that the lathe tool is properly adjusted is 94.7%
Related Questions
5⋅7⋅4=5⋅4⋅7is that associative property of multiplication or is itcommutative property of multiplication
What is a simplified expression for (x + y)-(x + y)?
Evaluate 3.2 + 6 to the second power minus 2 * 7.2 show your work will mark brainiest
A regular hexagon is shown below. Find the value of x.(11x + 21)°
a. Based on the reported sample mean and sample standard deviation, explain why it is not reasonable to think that the distribution of volunteer times for the population of South Korean middle school students is approximately normal.
b. The sample size was not given in the paper, but the sample size was described as large. Suppose that the sample size was 500. Explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal.
c. Calculate and interpret a confidence interval for the mean number of hours spent in volunteer activities per year for South Korean middle school children.
Answers
Answer:
a. If the distribution was normal, many values would be negative, what is incompatible with the response variable (hours dedicated to volunteer activities).
b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.
c. The 95% confidence interval for the mean is (13.307, 16.213).
Step-by-step explanation:
a. If the distribution was normal, the values with one or more standard deviation below the mean would be negative, what is incoherent for this case. This, in a normal distribution, represents approximately 16% of the values.
If we calculate the probabilty for a normal distribution with the sample parameters, the probability of having "negative hours" is 18.6% (see picture attached).
b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.
The sampling distribution standard deviation is also reduced by a factor of 1/√n.
c. We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=14.76.
The sample size is N=500.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The t-value for a 95% confidence interval is t=1.965.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the mean is (13.307, 16.213).
Answers
Answer:
-21
Step-by-step explanation:
1-2+4-8+16-32
=-21
Answer:
The sum of the first 6 terms of the infinite series will be - 21.
Step-by-step explanation:
In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,
Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,
1 - 2 + 4 - 8 + 16 - 32
= - 1 + 4 - 8 + 16 - 32
= 3 - 8 + 16 - 32 = - 5 + 16 - 32
= 11 - 32 = Solution : - 21
Answers
Answer:
where is the coordinate plane picture?
Step-by-step explanation:
Picture?
Answer:
You forgot to add the picture.
Step-by-step explanation:
Answers
Answer:
3.8a + 9b - 5.8
Step-by-step explanation:
distributing the negative
Answers
Answer:
Therefore, we conclude that the statement in (A) is incorrect.
Step-by-step explanation:
We have the following sentences:
A) If the probability of an event occurring is 1.5, then it is certain that event will occur.
B) If the probability of an event occurring is 0, then it is impossible for that event to occur.
We know that the range of probability of an event occurring is in the segment [0, 1]. In statement under (A), we have the probability that is equal to 1.5.
Therefore, we conclude that the statement in (A) is incorrect.
A. the number of guppies
B. the total number of fish
C. the number of non-guppies
( what is the variable in the problem?)
Answers
Answer:
6 non-guppies; C. the number of non-guppies
Step-by-step explanation:
13-7=x
(x is the number of non-guppies)
13-7=6