Long-term telemetry data from an autonomous drone fleet shows that 15% of flight missions result in a high-wind sensor alert. In a random selection of 50 flight missions, let HHH denote the number of missions that triggered a high-wind alert.
Write down a suitable distribution to model HHH.
State one assumption necessary for this model to be valid.
The probability that fewer than kkk missions result in a high-wind alert is less than 0.10.
Find the largest possible value of kkk.
A larger random sample of 200 missions is analyzed.
The probability that at least mmm of these missions result in a high-wind alert is 0.901, correct to 3 decimal places.
Using a suitable approximation, find the value of mmm.
The fleet undergoes a software optimization to better handle wind conditions. Subsequently, a random sample of 25 missions is taken and none of them (0) result in a high-wind sensor alert.
Test, at the 5% level of significance, whether there is evidence that the proportion of missions resulting in high-wind alerts has decreased. 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.