The distribution of resistance for resistors of a certain ty

The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance exceeding 10.634 ohms, and 5% having a resistance smaller than 9.7565 ohms. What are the mean value and standard deviation of the resistance distribution?

Solution

For 10% right tailed area, using a z table or technology,

z = 1.281551566

Thus, as

X = u + z s

10.634 = u + 1.281551566s [1]

Now, for 5% left tailed area, using a z table or technology,

z = -1.644853627

Thus,

9.7565 = u + (-1.644853627)s [2]

Solving system of equations [1] and [2],

u (mean) = 10.2497 [ANSWER]
s = 0.29986 [ANSWER]