When two average-height parents give birth to a child exhibiting achondroplasia, it is most likely due to a new mutation. this is because

The question already suggests the if the child has a genetic disease that both parents don't, there are only two possibilities: 

- the gene is recessive and both of the parents are carriers, but since they only have one of the genes, it doesn't manifest for them

- the gene is dominant - but then one of the parents  (or both) would have it too - so it must be a new mutation

it's caused by a dominant gene