The masses, in grams, of plums of a certain kind have the distribution \(\mathrm { N } ( 55,18 )\).
Find the probability that a plum chosen at random has a mass between 50.0 and 60.0 grams.
The heaviest \(5 \%\) of plums are classified as extra large.
Find the minimum mass of extra large plums.
The plums are packed in bags, each containing 10 randomly selected plums.
Find the probability that a bag chosen at random has a total mass of less than 530 g .
The masses, in grams, of apples of a certain kind have the distribution \(\mathrm { N } \left( 67 , \sigma ^ { 2 } \right)\). It is given that half of the apples have masses between 62 g and 72 g .
Determine \(\sigma\).