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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.