**Answer:**

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

**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 normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

**Central Limit Theorem**

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

**Mean of 15.4 inches, and standard deviation of 3.5 inches.**

This means that

**16 items are chosen at random**

This means that

**What is the probability that their mean length is less than 16.8 inches?**

This is the p-value of Z when X = 16.8. So

By the Central Limit Theorem

has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.