Applicants for a specialized coding bootcamp are screened for a specific learning aptitude. Historical data shows that the proportion of applicants identified as having this rare aptitude is 0.032.
Write down a suitable model for the distribution of the number of applicants identified with this aptitude from a total of nnn applicants.
State one assumption necessary for this distribution to be a suitable model of this situation.
Using a suitable approximation, find the probability that exactly 4 out of 150 applicants are identified as having this aptitude.
Explain why the approximation that you used in part (c) is appropriate.
An instructor claims that 80% of all accepted applicants successfully complete the advanced certification.
From a random sample of 120 accepted applicants, 88 successfully complete the certification.
Using a suitable approximation, test the instructor's claim at the 10% level of significance. State your hypotheses clearly.
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.