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?

Question

Quizplus · Accepted Answer

The Answer is Since 1.28 is the 90^th z percentile

\left( z _ { 1 } = 1.28 ight) ext { and } - 1.645 ext { is the } 5 ^ { th } z ext { percentile } \left( z _ { .05 } = 1.645 ight)

, the given information implies that

\mu + \sigma ( 1.28 ) = 10.634 ext { and } \mu + \sigma ( - 1.645 ) = 9.7565

, from which

\sigma ( - 2.925 ) = - .8775 , \sigma = .30 , ext { and } \mu = 10.25

The Distribution of Resistance for Resistors of a Certain Type