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Consider the given question,

The sample size is$24$.

First, we need to make sure that the z-test procedure is suitable for the given sample size. To use the z-test, we need to take care of the following conditions,

In case the sample size is $\left(n\right)<15$, then the z-test procedure can be used when the variable is very close to being normally distributed or normally distributed.

If the sample size is between $15<\left(n\right)<30$, then the z-test procedure can be used when there is no outlier in the data or the variable is far from being normally distributed.

If the sample size is greater than $30<\left(n\right)$, then the z-test procedure can be used without any limitation.

Here, the given sample size is small. This means, the sample size $\left(n\right)$is $24\left(<30\right)$.

The distribution of the variable is also highly skewed.

Hence, it can be said that the use of the z-test is inappropriate.