Question

Wires manufactured for use in a computer system are specified to have resistances between 0.14 and 0.16 ohms. The actual measured resistances of the wires produced by company A have a normal probability distribution with mean 0.15 ohm and standard deviation 0.005 ohm. (Round your answers to four decimal places.) (a) What is the probability that a randomly selected wire from company A's production will meet the specifications

Answer 1

Hence the probability that a randomly selected wire from company A's production will meet the specifications is 0.95455.

Explanation:

a)
`P(0.14 < x < 0.16 ) = P[(0.14 - 0.15)/ 0.005) < (x - \mu) /\sigma < (0.16 - 0.15) / 0.005) ]`

`=P(0.14 < x < 0.16 ) = P[(0.14 - 0.15)/ 0.005)< ((x - 0.15) /0.005) < (0.16 - 0.15) / 0.005) ]`

`=P(z<(0.01)/(0.005) )- P(z<-(0.01)/(0.005))`

Using z table,

= 0.9773 - 0.02275

= 0.95455.