State the conditions under which a normal distribution may be used to approximate a binomial distribution.
A botanist is testing the germination rate of a new hybrid seed variety. The probability of any individual seed germinating under standard conditions is 0.45.
For a batch of 20 seeds, determine the modal number of seeds that germinate. Justify your answer.
The random variable S S\,S represents the total number of seeds that germinate when 60 of these seeds are planted.
Find P(S<22)P(S < 22)P(S<22).
Given that exactly 12 seeds germinate from a specific batch of 20, find the probability that exactly 8 of these germinated from the first 14 seeds planted in that batch.
In a large-scale agricultural trial, 500 seeds are planted. Using a suitable approximation, find the probability that at most 235 seeds germinate.
