Final answer:
The inheritance pattern for neurofibromatosis in the family is autosomal dominant, indicated by the presence of café-au-lait spots and skin tumors in the boy and the tumor in his deceased brother.
Step-by-step explanation:
The inheritance pattern for neurofibromatosis in the described family is autosomal dominant. This is evidenced by the presence of characteristic symptoms such as café-au-lait spots and skin tumors (lumps and bumps) in the 15-year-old boy and the previous history of a tumor in his deceased brother. Since autosomal dominant conditions only require one copy of the faulty gene to be present for the disorder to manifest, it is likely that one of the parents carries the defective gene, even if they do not exhibit symptoms. Neurofibromatosis type I is known to be an autosomal dominant condition where those heterozygous for the gene (Nn) have the condition, and those homozygous for the normal gene (nn) do not.