The CDC reports that $25\%$ of baby boys $6-8$ months old in the United States weigh more than $20$ pounds. A sample of $16$ babies is studied.

a$.$ What is the probability that exactly $5$ of them weigh more than $20$ pounds?

b$.$ What is the probability that fewer than $3$ weigh more than $20$ pounds?

c$.$ What is the mean number who weigh more than $20$ pounds in a sample of $16$ babies aged $68$ months?

d$.$ What is the standard deviation of the number who weight more than $20$ pounds in a sample of $16$ babies aged $6-8$ months? Round your answer to four decimal places.