The lengths of Eastern bluebirds are normally distributed with mean 18.4 cm and standard deviation \(\sigma\) cm. It is known that 72% of Eastern bluebirds have length greater than 17.1 cm.

(b) Find the value of \(\sigma\).

A random sample of 120 Eastern bluebirds is chosen.

(c) Use an approximation to find the probability that fewer than 80 of these 120 bluebirds have length greater than 17.1 cm.