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

Answer:

The value is

 $P(X < 36) = 0.066807$

Step-by-step 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

     $P(X < 36) = P(\frac{X - \mu}{ \sigma } < \frac{ 36 - 37.5}{1} )$

$\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )$

    $P(X < 36) = P(Z < -1.5 )$

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

     $P(Z < -1.5) = 0.066807$

So

     $P(X < 36) = 0.066807$