1 The distribution of resistance for resistors of a certain

1. The distribution of resistance for resistors of a certain type is known to be normal, 10% of all resistance exceeding 10.256 ohms, and 5% have resistance smaller than 9.671 ohms. What are the mean value and standard deviation of the resistance distribution?

Solution

As

x = u + z * sigma

For the first case, the right tailed area is 0.10, thus, by table/technology, z = 1.281551566.

Thus,

10.256 = u + 1.281551566*sigma

For the second case, the left tailed area is 0.05. Thus, by table/technology, z = -1.644853627.

Thus,

9.671 = u + (-1.644853627)*sigma

Solving this system of equations,

u = 10.000
sigma = 0.200 [ANSWERS]