Using the Central Limit Theorem, it is found that since the sample size is greater than 30, a normal approximation can be used, hence the test can be made.
<h3>Central Limit Theorem</h3>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 sampling distribution is also approximately normal, as long as n is at least 30.
In this problem, the distribution of lengths is skewed, however, since the sample size is of 100 greater than 30, a normal approximation can be used, hence the test can be made.
To learn more about the Central Limit Theorem, you can check brainly.com/question/24663213