Question

over a long time, cable from acme cable co has a mean strength of 37.5 ksi with a known population standard deviation of 1 ksi. find the probability that a random piece of th ecable has a strength x lower than 36.0 ksi

Answer 1

The value is

`P(X < 36) = 0.066807`

Explanation:

From the question we are told that

The mean is
`\mu = 37.5 \ ksi`

The standard deviation is
`\sigma = 1 \ ksi`

Generally the probability that a random piece of the cable has a strength x lower than 36.0 ksi is mathematically represented as

`P(X < 36) = P((X - \mu)/( \sigma ) < ( 36 - 37.5)/(1) )`

`(X -\mu)/(\sigma )  =  Z (The  \ standardized \  value\  of  \ X )`

`P(X < 36) = P(Z < -1.5 )`

From the z table the probability of
`(Z < -1.5)` is

`P(Z < -1.5) = 0.066807`

So

`P(X < 36) = 0.066807`