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 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.