You are testing resistors and find they have a Gaussian distribution with a mean

Question

You are testing resistors and find they have a Gaussian distribution with a mean of 2200 ohm and a variance of 1500. Round numbers to the third decimal place. Use the Normal Distribution Table when directed. Solve for the probability that a resistor will have a resistance greater than 19000 and less than 2350 ohm. Use the Normal Distribution Table. Solve for the probability that a resistor will have a resistance greater than 20000. Use the Normal Distribution Table. Solve for the maximum resistance for the lower 15% of resistors. In other words, find the Distribution Table.

Explanation / Answer

The Gaussian is the same as the normal. Wikipedia can usually be trusted on this sort of question.

1. P(x>1900,x<2350)=P(z>1900-2200/150,z<2350-2200/150)=P(z>-2,z<1)=0.1814

2. P(x>2000)=P(z>-1.33)=0.9082

3. P(X<x)=0.15

so z=-1.036=x-2200/150

x=2044.6

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