Question
In: Statistics and Probability
A machine at Katz Steel Corporation makes 4-inch-long nails. The probability distribution of the lengths of...
A machine at Katz Steel Corporation makes 4-inch-long nails. The probability distribution of the lengths of these nails is approximately normal with a mean of 4 inches and a standard deviation of 0.08 inch. The quality control inspector takes a sample of 25 nails once a week and calculates the mean length of these nails. If the mean of this sample is either less than 3.95 inches or greater than 4.05 inches, the inspector concludes that the machine needs an adjustment. What is the probability that based on a sample of 25 nails, the inspector will conclude that the machine needs an adjustment?
Round your answer to 4 decimal places.
Probability =
Solutions
Expert Solution
Solution: 
Explanation:
It is given that the probability distribution of the lengths of these nails is approximately normal with a mean of 4 inches and a standard deviation of 0.08 inch. Therefore, we have:
It is also given that the inspector concludes that the machine needs an adjustment if the mean of the sample is either less than 3.95 inches or greater than 4.05 inches
We are required to find the probability that based on a sample of 25 nails, the inspector will conclude that the machine needs an adjustment. Therefore, we have to find:
orchestra answered 1 year agoRelated Solutions
A machine at Katz Steel Corporation makes 4-inch-long nails. The probability distribution of the lengths of...
A machine at Katz Steel Corporation makes 4-inch-long nails. The
probability distribution of the lengths of these nails is
approximately normal with a mean of 4 inches and a standard
deviation of 0.10 inch. The quality control inspector takes a
sample of 16 nails once a week and calculates the mean length of
these nails. If the mean of this sample is either less than 3.96
inches or greater than 4.04 inches, the inspector concludes that
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A machine at Katz Steel Corporation makes 5-inch-long nails. The probability distribution of the lengths of...
A machine at Katz Steel Corporation makes 5-inch-long nails. The
probability distribution of the lengths of these nails is
approximately normal with a mean of 5 inches and a standard
deviation of 0.08 inch. The quality control inspector takes a
sample of 16 nails once a week and calculates the mean length of
these nails. If the mean of this sample is either less than 4.95
inches or greater than 5.05 inches, the inspector concludes that
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A machine at Katz Steel Corporation makes 3-inch-long nails. The probability distribution of the lengths of...
A machine at Katz Steel Corporation makes 3-inch-long nails. The
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deviation of 0.08 inch. The quality control inspector takes a
sample of 16 nails once a week and calculates the mean length of
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A machine produces 3-inch nails. A sample of 10 nails is obtained and the lengths determined....
A machine produces 3-inch nails. A sample of 10 nails is
obtained and the lengths determined. After some calculation, the
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Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine...
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the machine is working properly, the mean length of the rods is 36
inches. The standard deviation of the lengths of all rods produced
on this machine is always equal to 0.035 inch. The quality...
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine...
Lazurus Steel Corporation produces iron rods that are supposed
to be 36 inches long. The machine that makes these rods does not
produce each rod exactly 36 inches long. The lengths of the rods
are normally distributed and vary slightly. It is known that when
the machine is working properly, the mean length of the rods is 36
inches. The standard deviation of the lengths of all rods produced
on this machine is always equal to 0.035 inch. The quality...
Lazurus Steel Corporation produces iron rods that are supposed to be 33 inches long. The machine...
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On June 1, 2014, Montreal Corporation purchased a machine to process steel. The machine that cost...
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Describe the point estimate, normal probability distribution, and standard normal probability distribution in details, in 4 paragraphs.
Empolyee
age
1
25
2
32
3
26
4
40
5
50
6
54
7
22
8
23
age
Mean
34
Standard Error
4.444097209
Median
29
Mode
#N/A
Standard Deviation
12.56980509
Sample Variance
158
Kurtosis
-1.152221485
Skewness
0.767648041
Range
32
Minimum
22
Maximum
54
Sum
272
Count
8
Confidence Level(95.0%)
10.50862004
Describe the point estimate, normal probability distribution, and standard normal probability distribution in details, in 4 paragraphs.
A steel factory produces iron rods that are supposed to be 36 inches long. The machine...
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lengths of these rods vary slightly.
It is known that when the machine is working properly, the mean
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According to design, the standard deviation of the lengths of all
rods produced on this machine is
always equal to .05 inches. The quality control...
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