Answer:
30.51% probability that the average length of a randomly selected bundle of steel rods is between 219.7-cm and 220-cm.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
In this problem, we have that:
Find the probability that the average length of a randomly selected bundle of steel rods is between 219.7-cm and 220-cm.
This is the pvalue of Z when X = 220 subtracted by the pvalue of Z when X = 219.7.
X = 220
By the Central Limit Theorem
has a pvalue of 0.8051
X = 219.7
has a pvalue of 0.5
0.8051 - 0.5 = 0.3051
30.51% probability that the average length of a randomly selected bundle of steel rods is between 219.7-cm and 220-cm.
