Each year, a detailed study is conducted on a random sample of 36 Lorenz birdwing butterflies in Town A. A Lorenz birdwing butterfly is considered to be very large if its wingspan is greater than 17.5 cm. The probability that the wingspan of any Lorenz birdwing butterfly in Town A is greater than 17.5 cm is 0.0527, correct to four decimal places. For random samples of 36 Lorenz birdwing butterflies in Town A, is the random variable that represents the number of butterflies that are very large.
The probability that or more butterflies, in a random sample of 36 Lorenz birdwing butterflies from Town A, are very large is less than 1%. Find the smallest value of , where is an integer.
Is it correct to think it as to find the smallest integer such that 36C * 0.0527^k * (1-0.0527)^36-K < 1% ? If so, how should I calculate it?
Note: (36C as in choose from 36 with replacement)