In an ecological study of a specific butterfly population, it is found that 35% of the individuals carry a specific genetic marker, denoted by WWW. A researcher captures a random sample of 30 butterflies. Let the random variable XXX represent the number of butterflies in the sample who carry marker WWW.
Find (i) P(X=12)P(X = 12)P(X=12) (ii) P(X>8)P(X > 8)P(X>8) (iii) the smallest value of kkk such that P(X≤k)≥0.75P(X \le k) \ge 0.75P(X≤k)≥0.75
The study expands to a much larger region, and a new random sample of 400 butterflies is collected.
(i) Using a suitable normal approximation, find the probability that no more than 130 of these 400 butterflies carry marker WWW. (ii) Justify why a normal approximation is appropriate in part (b)(i).
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.