SOLUTION: The lengths of nails produced in a factory are normally distributed with a mean of
4.95 centimeters and a standard deviation of
0.05 centimeters. Find the two lengths that sep
Algebra.Com
Question 1019893: The lengths of nails produced in a factory are normally distributed with a mean of
4.95 centimeters and a standard deviation of
0.05 centimeters. Find the two lengths that separate the top
5% and the bottom
5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
The lengths of nails produced in a factory are normally distributed with a mean of
4.95 centimeters and a standard deviation of
0.05 centimeters. Find the two lengths that separate the top
5% and the bottom
5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Solution:
The top and bottom 5% can be obtained as a multiple of the standard deviation (σ) using the normal distribution curve, and the definition of Z=(X-μ)/σ.
From normal distribution tables, the 95% and 5% cutoffs are Z=±1.65.
Since Z=(X-μ)/σ, we solve for X in terms of Z
X=±1.65σ+μ
=5.95±1.65*0.05=(4.868,5.032)
are the limits to the 5-95% bracket of lengths.
RELATED QUESTIONS
The lengths of nails produced in a factory are normally distributed with a mean of 6.02... (answered by stanbon)
the number of nails of a given length is normally distributed with a mean length of 5 in. (answered by edjones)
The number of nails of a given length is normally distributed with a mean length of 5.00... (answered by Boreal)
A company manufacture nails using two machines (two technologies) bearing the same cost... (answered by ewatrrr)
the lengths of steel rods cut by a machine are normally distributed with mean 13.8com. It (answered by stanbon)
The lengths of lumber a machine cuts are normally distributed with a mean of 93 inches... (answered by ikleyn)
The lengths of brook trout caught in a certain Colorado stream are normally distributed... (answered by Fombitz)
The lengths of marbles are normally distributed with a mean of 3.9m and a standard... (answered by Fombitz)
The numbers of cookies in a shipment of bags are normally distributed, with a mean of 48... (answered by rapaljer)