Final answer:
Calculating the probability of at least 40 out of 50 carrot seeds germinating involves using the binomial distribution formula to sum the individual probabilities of 40, 41, ..., up to 50 seeds sprouting. The germination rate of each seed is 92%.
Step-by-step explanation:
The subject of the question is Mathematics, specifically related to probability theory. The probability of a packet of carrot seeds with a germination rate of 92% resulting in at least 40 seedlings from a row of 50 seeds must be calculated. To answer this, one can use the binomial distribution formula, which is applicable for a fixed number of independent trials, each with the same probability of success.
In this case, the success is the germination of a seed with a probability of 0.92, and the number of trials is 50. The question asked requires the probability of at least 40 successes (seedlings), which means calculating the cumulative probability of getting 40, 41, 42, ..., up to 50 successfully germinated seeds. This can be done using statistical software or a binomial probability table, as manually calculating each probability and then summing them could be quite cumbersome.
However, to find the exact probability, one would need to use the binomial probability formula P(X = k) = (n choose k) * pk * (1-p)n-k, where 'n' is the number of trials, 'k' the number of successes, and 'p' the probability of success on a single trial, summing the probabilities for k = 40 to k = 50.