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, $p$ , of fragment-type microplastics has decreased from the usual 0.42.

She tests the hypotheses:

H_0: p = 0.42

H_1: p < 0.42

She takes a random sample of 400 particles and finds that $x\,$ of them are fragments.

(i) Using a 5% level of significance and a normal approximation, find the critical region for $x$ .

(ii) In her sample, she finds 150 fragments. Complete the test, stating your conclusion in context.

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, $p$ , of fragment-type microplastics has decreased from the usual 0.42.

She tests the hypotheses:

H_0: p = 0.42

H_1: p < 0.42

She takes a random sample of 400 particles and finds that $x\,$ of them are fragments.

(i) Using a 5% level of significance and a normal approximation, find the critical region for $x$ .

(ii) In her sample, she finds 150 fragments. Complete the test, stating your conclusion in context.

2.4.13 Model with probability distributions

Question 13

Markscheme

2.4.13 Model with probability distributions

Question 13

Markscheme

2.4.13 Model with probability distributions

Question 13

2.4.13 Model with probability distributions Questions

2.4.13 Model with probability distributions

Question 13

2.4.13 Model with probability distributions Questions