A marine biologist is analyzing the composition of microplastics found in sediment samples from a specific coastal region. She categorizes the particles into four types based on their morphology.
The distribution of these types among the collected particles is shown in the following table:
| Particle Type | Microbeads | Fragments | Fibers | Pellets |
|---|---|---|---|---|
| Probability | 0.18 | 0.42 | 0.30 | 0.10 |
Samples are processed in batches of 150 particles.
Using a suitable approximation, find the probability that in a single batch:
(i) there are exactly 30 microbeads.
(ii) there are at most 55 fibers.
(iii) there are at least 95 particles which are not fragments.
The biologist investigates a different coastal region where she suspects the proportion, ppp, of fragment-type microplastics has decreased from the usual 0.42.
She tests the hypotheses:
H0:p=0.42 H_0: p = 0.42 H0:p=0.42 H1:p<0.42 H_1: p < 0.42 H1:p<0.42She takes a random sample of 400 particles and finds that x x\,x of them are fragments.
(i) Using a 5% level of significance and a normal approximation, find the critical region for xxx.
(ii) In her sample, she finds 150 fragments. Complete the test, stating your conclusion in context.
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.