Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 236.8-cm and a standard deviation of 1.3-cm. For shipment, 29 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 236.5-cm and 236.7-cm. P(236.5-cm < M < 236.7-cm) =

Answer 1

0.0606. .

hope this helps

Answer 2

Transform M to the standard normally distributed random variable Z via

`Z=(M-\mu_M)/(\sigma_M)`

where
`\mu_M` and
`\sigma_M` are the mean and standard deviation for
`M`, respectively. Then

`P(236.5<M<236.7)=P(-0.2308<Z<-0.0769)\approx\boxed{0.0606}`