Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 119.7-cm and a standard deviation of 2-cm. For shipment, 30 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 119.8-cm.
P(M < 119.8-cm) =

Answer 1

A company produce steel rods. The lengths of the steel rods are normally distributed with mean of 119.7 cm and a standard deviation 2 cm. For shipment, 30 steel rods are bundle together. We select a bundle randomly.

Now, we want to find the probability that average length of selected bundle is less than 119.8 cm. i.e we want to find P(M < 119.8cm)

We define a Random variable,

X_{​​​​​​i} = length of i^{​​​​​​th}​ rod of selected bundle.

And X_{​​​​​​i} ~ N(119.7, 2) [given]

[ value of phi(0.2739) = 0.6064 is taken form standard normal probability table]

Ans:- So the required probability,

P(M < 119.8cm) = 0.6064