(a)[4]
How many of these $150$ birds would you expect to have a length between $15.4\text{ cm}$ and $16.8\text{ cm}$?
(b)[3]
The lengths of Eastern bluebirds are normally distributed with mean $18.4\text{ cm}$ and standard deviation $\sigma\text{ cm}$. It is known that $72\%$ of Eastern bluebirds are longer than $17.1\text{ cm}$. Find the value of $\sigma$.
(c)[5]
A random sample of $120$ Eastern bluebirds is selected. Use an approximation to determine the probability that fewer than $80$ of these $120$ bluebirds have length greater than $17.1\text{ cm}$.