Question

a produce manufacturer fills bags of baby carrots by weight. each bag is supposed to have 12 ounces of baby carrots. unfortunately, 3% of the baby carrots are discolored. let x represent the number of discolored baby carrots in a bag. are the conditions for a binomial setting in this scenario met? no, there is no fixed number of baby carrots. yes, all four conditions in bins have been met. no, we are sampling the carrots without replacement. no, 3% is a very small probability, so we should not carry out a binomial procedure.

Explanation:

For a binomial setting, the BINS conditions are:

• Binary outcomes (discolored or not discolored).
• Independent trials (assuming the presence of one discolored carrot doesn't affect another, which is a reasonable assumption in large - scale production).
• Number of trials is fixed (each bag has a fixed number of baby carrots, since they are filled by weight and each bag is supposed to have a consistent amount).
• Success probability is constant (3% of baby carrots are discolored, so the probability of a "success" (finding a discolored carrot) is constant for each trial).

Answer:

Yes, all four conditions in BINS have been met.