An automated agricultural research system monitors large batches of seedlings for a rare genetic mutation. This mutation occurs independently in each seedling with a probability of 0.08.
Determine the probability that in a randomly selected batch of 25 seedlings, exactly 3 will possess this mutation.
Batches are grouped into larger delivery trays, each containing 50 seedlings. A quality control inspector selects 5 of these trays at random.
Find the probability that exactly two of these trays will contain more than 6 seedlings with the mutation.
A high-capacity growing facility contains n n\,n seedlings of a different strain, where the probability of the mutation is 0.2.
Using a normal approximation, the probability that this facility contains more than 91 seedlings with the mutation is 0.0749.
Find the value of nnn.
