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 :(
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
My answer: 0.3413
Please check my workings if there is anything wrong with it. Thank you!