Statistics - CLT

Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 243.5-cm and a standard deviation of 0.8-cm. For shipment, 24 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 243.5-cm.

P(M > 243.5-cm) 

Answer 1

It is the distribution of sample means that follows a Gaussian distribution with mean equal to μ and standard deviation equal to δ/(n^1/2). With n=24 being the sample size, μ=243.5, δ=0.8, we have:

P (M > 243.5) = 0.5.

In fact, every Gaussian distribution presents 50% of probability to be higher or lower than the average. That's a property.