A bakery produces loaves of bread whose weights, WWW grams, follow a normal distribution with mean 800 g800\text{ g}800 g and standard deviation 25 g25\text{ g}25 g.
Estimate the proportion of loaves that weigh more than 840 g840\text{ g}840 g.
The bakery classifies loaves into three categories: Small, Standard, and Large, such that there is an equal proportion of loaves (exactly 13\frac{1}{3}31) in each category.
Find the weight limits that define the 'Standard' category.
A loaf is selected at random from the 'Large' category.
Find the probability that this loaf weighs less than 830 g830\text{ g}830 g.
A customer selects a random sample of 3 loaves from the bakery's total production.
Find the probability that there is exactly one loaf from each of the three categories.
