(a)[4]
From a random sample of $500$ of these small rice bags, what number would you expect to have a mass greater than $1.26\text{ kg}$?
(b)[3]
The masses of the large bags of rice are normally distributed with mean $2.50\text{ kg}$ and standard deviation $\sigma\text{ kg}$. $20\%$ of these large bags of rice have a mass less than $2.40\text{ kg}$. Determine $\sigma$.
(c)[5]
A random sample of $80$ large bags of rice is selected. Use an appropriate approximation to find the probability that fewer than $22$ of these large bags of rice have a mass less than $2.40\text{ kg}$.