# Gaussian (Normal) Distribution (LEVEL 2 CALCULUS)

• Apr 23rd 2011, 02:08 PM
Salcybercat
Gaussian (Normal) Distribution (LEVEL 2 CALCULUS)
Hello! These are the questions:

1. Nominally 1\mu Farad capacitors are found to have values that are normally distributed. They are marked as being +- 5% tolerance, but 20% are found to be outside this range. What is the standard deviation of the production spread?

My solution is provided below. I really do hope some of you can help. It's Easter break and all the tutors are away :(

http://i51.tinypic.com/15o761k.jpg

EDIT: There has been a careless mistake. 80% values are found to be inside the range so it should be 0.8 not 0.08. A (referring to the area on one side of the curve that is out of range) = 0.5-0.4 =0.1
By referring to the table, A of 0.1 would refer to z = 0.26.
Standard deviation would be = |(0.95 - 1)|/(0.26) = 0.2
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2. A d.c signal of 100mV has added noise whose amplitude p.d.f is Gaussian with zero mean and variance 10^-6 [V^2]. This signal is fed into a D.V.M with resolution 1mV, which rounds to the nearest 0.5mV. Calculate the probability of the meter reading 101 mV

http://i56.tinypic.com/15o8ras.jpg

Please check my workings if there is anything wrong with it. Thank you!
• Apr 23rd 2011, 03:07 PM
Effendi
According to my table z = -1.28 has a lower tail proportion of 10%, so z = $\pm$1.28. You converted 80% to decimal format wrong, 0.8 not 0.08. So 0.8 divided by two yields 0.4, 0.5 - 0.4 = 0.1 . You just ended up off by a magnitude.
• Apr 23rd 2011, 03:10 PM
Salcybercat
Oh thank you, that was a very careless mistake! :p
Is that my only mistake? Because I still can't get the answer.

To edited A would be 0.5 - 0.4 =0.1
Based on the table, z would be about 0.25.

Using that information, I would get a standard deviation of 0.2
• Apr 23rd 2011, 04:04 PM
Effendi
Everything else you did before was right. A z value of -0.25 has about 0.4 to the left, 0.25 has about 0.4 to the right, but the outside has 0.1 to either side, both sides together is 0.2, meaning 0.8 (80%) on the inside, which is correct. I think your looking for the wrong proportion, you looked up 0.4, you should have looked for a proportion of 0.1. What is A? Is A the proportion to the left of the given z value?
• Apr 23rd 2011, 04:12 PM
Salcybercat
A is basically 'area', sorry to have confused you. Yes I did look for a proportion with area =0.1026. According to the table, z would be equal to 0.26. The standard deviation would be (0.95-1)/0.26 = about 0.2. Did I calculate something wrong?
• Apr 23rd 2011, 04:16 PM
Effendi
A is area, is it the area of the region z distance from the mean? Is it area of the region to the right of a z value? Is it area to the left of a z value? Did you look up 0.1026 because it's the closest the table has to 0.1?
• Apr 23rd 2011, 04:40 PM
Effendi
I took another look and you did do something else weird, "For A = 0.46 Based on table, z = 1.7". On the table 1.7 corresponds to an A value of .0446, are you dyslexic? That would explain your other mistake.
• Apr 24th 2011, 02:22 AM
Salcybercat
A = area is the region from 0, which would mean it is the region to the left of z. Yes I did look up 0.1026 since that's the closest to 0.1, which would refer to z being 0.26.
No, I'm not dyslexic. z=1.7 does refer to A=0.46. I think you made a mistake reading the table. I've provided a snapshot of the table, proving your method wrong. But anyway we're not using A=0.46. The A we're using is A=0.1 now

http://i52.tinypic.com/4hzi3p.jpg
• Apr 24th 2011, 03:46 AM
Effendi
Our tables are different, and I'm sorry that was rude of me. So if I understand correctly and your table gives the distance from zero to z, you need to look up the z value which corresponds to an A value of 0.4, 0.4 because 0.4 is half the internal area. And then just use the z value in the same formula as you used before to find the standard deviation. That picture cleared things up, my table gives the area of the entire tale to the left of z.
• Apr 24th 2011, 06:23 AM
Salcybercat
It's okay, no offense taken :) So my mistake was taken A=0.1, instead I should take refer to the area of 0.4. I've come across another Gaussian question I couldn't answer. If you have some time to spare, please take a look at it (The first post: I added another question)