An article in the Los Angeles Times $($Dec$.3,1993)$ reports that $1$ in $200$ people carry the defective gene that causes inherited colon cancer. In a sample of $1000$ individuals, what is the approximate distribution of the number who carry this gene? Use this distribution to calculate the approximate probability that

a$.$ Between $5$ and $8($inclusive$)$ carry the gene.

b$.$ At least $8$ carry the gene.