The length of the Pacific sardine (Sardinops sagax) can be considered a random variable with normal distribution with mean 175 mm and standard deviation 25.75 mm.\ a) (1 point) A canning company for this variety of sardines only accepts as quality sardines those with a length greater than 16 cm. What percentage of the sardines caught by a fishing vessel will be of the quality expected by the canning company?\ b) ( 0.5 points) Find a length t $< 175 \mathrm {~mm}$ such that between t and 175 mm there are 18\% of the sardines caught.\ c) (1 point) At sea, sardines are processed in batches of 10. Subsequently, sardines from each batch that are smaller than 15 cm are returned to the sea as they are considered small. What is the probability that in a batch there is at least one sardine returned as small?
The length of the Pacific sardine (Sardinops sagax) can be considered a random variable with normal distribution with mean 175 mm and standard deviation 25.75 mm.\
a) (1 point) A canning company for this variety of sardines only accepts as quality sardines those with a length greater than 16 cm. What percentage of the sardines caught by a fishing vessel will be of the quality expected by the canning company?\
b) ( 0.5 points) Find a length t $< 175 \mathrm {~mm}$ such that between t and 175 mm there are 18\% of the sardines caught.\
c) (1 point) At sea, sardines are processed in batches of 10. Subsequently, sardines from each batch that are smaller than 15 cm are returned to the sea as they are considered small. What is the probability that in a batch there is at least one sardine returned as small?