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

Transform M to the standard normally distributed random variable Z via

$Z=\dfrac{M-\mu_M}{\sigma_M}$

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

$P(236.5$