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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.