You are working quality control for a manufacturer of screws. You are sampling a particular screwas it comes off of the line. You expect the length of the screw to followa normal distribution asfollows, where the mean and standard deviation are expressed in centimeters (cm)150(z-2)2p(x)0.1 2T1. What is the mean of the screw length?2. What is the standard deviation of the screw length?3. At whatvalue does the corresponding bell curve have its absolute maximum?4. At whatvalues does the corresponding bell curve have its points of inflection?5. What is the probability that a screw length will be between 1.8 and 2.2 cm?

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Asked Oct 20, 2019
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You are working quality control for a manufacturer of screws. You are sampling a particular screw
as it comes off of the line. You expect the length of the screw to followa normal distribution as
follows, where the mean and standard deviation are expressed in centimeters (cm)
1
50(z-2)2
p(x)
0.1 2T
1. What is the mean of the screw length?
2. What is the standard deviation of the screw length?
3. At what
value does the corresponding bell curve have its absolute maximum?
4. At what
values does the corresponding bell curve have its points of inflection?
5. What is the probability that a screw length will be between 1.8 and 2.2 cm?
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You are working quality control for a manufacturer of screws. You are sampling a particular screw as it comes off of the line. You expect the length of the screw to followa normal distribution as follows, where the mean and standard deviation are expressed in centimeters (cm) 1 50(z-2)2 p(x) 0.1 2T 1. What is the mean of the screw length? 2. What is the standard deviation of the screw length? 3. At what value does the corresponding bell curve have its absolute maximum? 4. At what values does the corresponding bell curve have its points of inflection? 5. What is the probability that a screw length will be between 1.8 and 2.2 cm?

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Step 1

As per norms, the first three questions are answered. The problem concerns normal distribution of a random variable representing the length of a random screw.

 

Step 2

If X is a random variable assuming continuous values (like the length in this problem) , the probability that it assumes values between a and b is obtained by integrating the probability density function p(x) between a and b.

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Xa continuous random var iable. Then Pr ob(a< X<b)px)cdx

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Step 3

One instance  is a normally distributed random...

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(2-p) 202 Ov2 = Mean Standard Deviation Normal distibution curve

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Calculus

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